The fuel capacity, armament, armor, and overall weight would be the remaining factors here, and are the real-world factors that already DID plague the P-40, particularly with the more substantial changes to the airframe the P-40D and later models saw. (lots of weight gain there, changing of the cockpit position, canopy, fuel tanks, new wing with .50" gun mounts -and initially hispano mount provisions in the D model- tons of weight gain due to structural redesigns, larger radiator and oil coolers, and added armor, modest gain in fuel capacity over the P-40C and loss over the P-40B -with its metal tanks and linatex style self sealing coating- or Hawk 75A-2, plus later extended rear fuselage to accomodate the Merlin's added weight iirc)
The critical factors here could ALSO have benefited the P-40 itself, careful attention to detail in keeping weight down, selecting armament optimized for fighter vs fighter combat (and lightly built bombers) over bomber interception, etc. (though the point was already made for the superiority of the .50 BMG during the BoB -or when employed against any linatex -or laminated leather- style external self sealing material on metal tanks, not well suited to 13 mm projectiles, let alone 20 mm -explosive and incendiary properties aside)
On armament: It should also be noted that it was the British, not the Americans that insisted on mounting more guns on the Kittyhawk/Warhawk, Wildcat/Martlet, and Mustang. Many Navy pilots preferred the 4-gun arrangement of the F4F (though the issues with kinks and jams in the F4F-3's installation weren't ideal, the lower weight and particularly higher ammunition capacity were preferred) this may also have been less from British Pilot preference, and more Air Ministry doctrine/thinking. (the Mustang I's 2x .303 and 4x .50 BMG would probably have served fine stripped to just 4x 50s, 2 synchronized, 2 in the wings -A-36 crews often removed the synchronized guns but that was with 4 .50 cal guns already in the wings) The P-51A, B, and C all sported 4 gun armaments and it wasn't until the D that the array of 6 became standard. (by which time it was more genuinely needed if still not always superior to the 4-gun arrangement, though the D was also heavier and poorer performing than the B/C for more reasons than the armament)
Improvements in the browning to up rate of fire (similar to the FN Browning) would have helped with synchronization losses too, even if such boosted speeds were witheld from standard unsynchronized use for conservative wear/reliability reasons. (even with the slower RoF, the nose mounted arrangement had advantages, especially if you could do away with wing guns entirely -mixed wing and nose guns is a bit less nice and takes training for both sorts of convergence and gunnery to make good use of, unlike the P-38 -the only all-nose armmed USAAF fighter) On the plus side, 550-600 RPM would reduce the barrel-burning nature of the M2 if fired too long. (for pilots a bit more naturally heavy on the trigger)
Starting with the Tomahawk as the base, adapting the wings to carry 1 .50 cal gun each (for a F2A-2 style armament) would have been a good compromise, but with the radial engine it might be possible to add 2 more .50s to the fuselage sides and go all-nose without much increase to drag, or any at all if hidden in the expanded fuselage sides along with turbo-supercharger outlet ducting. (obviously positioning the guns to avoid barrel heating of that air flowing into the nose intercoolers) With the Allison's change in nose geometry with the F-series, the guns would probably have to be omitted from the over-cowl position and possibly introduced under fuselage embedded above the radiator as well as 2 in the fuselage sides. (or possibly all four in the fuselage sides as cheek mounts, or ... in the case of a turbocharged V-1710, embedded in the fuselage 'cheeks' themselves caused by the necessary ducting)
Avoiding wing mounted guns also frees up a lot of space for potential fuel tankage without having to engineer fuel cell compartments around weapons compartments (and possibly be forced to add more mass outboard of the wing and compromise roll rate). Fuel tanks added to the region the wing guns would otherwise be (particularly all the useful space towards the center and leading edge of the thicker, inboard portion of the wing just outboard of the wheel housing) and could make the fighter into a good long-range intruder or high altitude escort fighter. (in the case of turbocharging or decent 2-stage supercharing ... or some proper refinement of a single stage allison supercharger to match/beat the Merlin rather than sticking with the known faults in favor of volume production -not to mention securing more funds to properly test WEP earlier and possibly even clear overrev for WEP) Leaving space for wing-mounted radiators would also be a huge help in reducing the P-40's drag, especially with the larger radiators needed to use power settings much beyond the old C series (V-1710-33)
Also remember how limited the armament of the BF-109F was and still somewhat modest 2x MG 131 and 1x MG 151/20 configuration. (4x synchronized .50s in the nose would be a fair match for that, especially given the Curtiss built fighters would be more rugged due to typical aggressive USAAF structural requirements)
On top of all that, remember the intrinsic adantages the P-36 and P-40 held over the Spitfire and Bf 109 (and to lesser extent 190 .... and massive effect Hurricane, Zero, and Oscar): exceptional roll rate, light controls at all speeds (but especially so at high speeds) and ability to out-maneuver other aircraft in similar ways to the P-47. This is important as it also meant that even in overweight configurations, the added dive 'thrust' of that weight could be exploited to full extent rather than having controls freeze up during a power dive. This is also a good reason to avoid putting lots of added weight in the outboard wing sections. (aside from perhaps tip-tanks ... in hindsight given their tendency to have winglet-like properties that reduce drag and increase aileron effectiveness -and thus roll rate when not filled with fuel)
The P-36/P-40 airframe was generally very clean and well designed for its era, cleaner than the P-43, F4F, F2A, and cleaner than the 109 and spitfire (look at the speeds it managed in spite of being overweight and underpowered). The F2A was never fitted with an R-1830, so the potential drag improvements there are harder to guess (performance with roughly similar R-1820s seems in the ballpark, but the F2A has a bulkier fuselage -if still much slimmer than P-43 and F4F- so it's harder to make even a general guess to that sort of pairing, plus the F2A had a smaller wing, but high-lift high-drag airfoil and thicker 18% root -then again, so did the F4U) I will say the P-36 benefitted more from the R-1830's slim size than the F4F did (which gained very little indeed given its large overall diameter and bulk -and wing area, when comparing R-1820s and 1830s of similar power/altitude performance) and the P-36 airframe almost certainly wouldn't have been as well matched to the FM-2's powerplant than the Wildcat was. (and for that matter, the non-water-injected earlier models of similar power at alitude could have been used on the F4F with little loss over the 2-stage R-1830 while the P-36 would gain far more from the drag reduction, especially with the eventual refinements offered by the XP-42 program -albeit more likely in time to be adopted with the R-2000)
And all that said, a final comment on a potentially more useful alternate use of Curtiss manufacturing and design ability: instead of second-sourcing the P-47, they could have taken on the task of developing a turbo-less P-38 derivative for medium/low-altitude duties (extremely useful in the MTO and PTO both as a fighter and fighter-bomber -though prior to those theaters becoming obvious in general, such a performance realm WAS the preferred specification for USAAF fighters pre-war, with a greater emphasis on cooperation and ground-attack ability). The P-38 was more expensive than the P-47 (and much more so than the P-40) true, but a stripped down derivative would be somewhat cheaper and more so easier to maintain and operate while also totally sidestepping the turbocharger problems the early P-38s were having on top of the compressibility issues far far worse in the high altitude flight envelope over Europe (due to cold and thin air allowing faster acceleration in a dive and lower ambient speed of sound). If that program was organized early enough, it might have even been possible to have a Curtiss P-38 accepted for operational duty before the P-38F arrived ... really it's not all that hard given just now long it took the P-38 to even get that far. (with Curtiss ignoring all but the problems relevant to operation at/below 15,000 ft or somewhat higher in warm climates -lack of heating and mach-tuck issues both avoided, they could have started shifting manufacturing and tooling up for the P-38 based on earlier models with only a few final detail changes left open to fix, particularly the wing fillet additions that eliminated the buffeting problem, while applying their experience with the P-40's intake/exhaust design to make a pretty efficient turbo-less nacelle for the P-38)
Given the problems the P-47G suffered this might have been no more foolproof, but it seems at least possible that they'd have fared better (and had somewhat more in common with P-40 experience and prior work) with the P-38. Second-sourcing the P-39 might have been more trouble too given its heavier use of new/novel technology than the P-38. (all the electrical equipment with miles of wiring -literal miles I believe- and some specialized modular mass production techniques for the airframe itself that worked very well for Bell but might not have been so nice for Curtiss)
In a best-case scenario, Curtiss engineers working on solving some of the P-38's problems independently of Lockheed might have been able to speed up progress on both fronts, sharing findings with Lockheed while keeping up with progress on that end as well. (plus, I believe the P-38 and P-40 already had some parts commonality in the curtiss electric propellers used on some models ... in fact the retention of that rather small 3-blade Curtiss-electric propeller late in the P-38's run has been criticized for being too small to properly take advantage of the added engine power, while the same has been argued against Curtiss for retention of that aging unit on the P-40 -the P-39, P-51, and P-47 all went though multiple propeller changes to rather significant degree while the P-38K's larger area 3-blade prop was refused for production due to delays on the assembly line it would cause ... not sure if any 4-blade props might have avoided that by retaining similar spinner diameter -the P-51 and P-39 both avoided nose geometry redesigns by keeping any prop/hub/spinner changes to ones compatible with the existing geometry) The P-40D and YP-38 obviously had to change nose/nacelle/spinner geometry due to the engine dimension and thrust-line changes ... and I assume lowering the engine mount to maintain the P-40B/C thrust line would have been more problematic. (or ... maybe it wouldn't have been if they'd moved the radiator(s) to the wings, allowing the upper nose geometry to remain more constant along with the thrust line ... and had more room at the top of the engine for cowl-mounted .50s)
Hmm, actually, yes, maintaining a more Tomahawk-like fuselage/nose structure and fitting a row of 4 guns to the nose top and/or sides (or possibly even 6 later on when the added firepower was needed) and relocating the radiators to the wing or wing center section (and making up the center section fuel space with wing-mounted cells) would have been one of the better options for the Allison powered P-40 as well, with or without turbocharger.
And some useful cross-sections of the P-40, Hawk-75, and P-47 for reference.
http://www.histaviation.com/Hawk_75_A-2_Drawing_1424x926.jpg (fuel tank capacity listed too -appears identical to the P-40B's arrangement with a total of 135 imp gal or 162 US gal)
http://images.fineartamerica.com/images-medium-large/p-40-tomahawk-iib-science-source.jpg (equivalent to the P-40C, note the modified fuel tank arrangements -these should be proper self-sealing cells, not modified metal tanks like the P-40B and Tomahawk IIA, with fuel capacity of 134 US Gallons or approximately 112 imp gal)
https://s-media-cache-ak0.pinimg.com/736x/f9/37/d0/f937d068f17625f9fb18c3f0986b87e2.jpg
P-40E 122.8 imp gallon capacity or 147.4 US gal (I believe it's officially 148 US gal, and slightly off due to rounding errors partially on the part of those imperial figures)
http://www.wardrawings.be/WW2/Image...-USA/Files/1-Fighters/P-47/Boards/Board-2.jpg
http://www.airwar.ru/image/idop/fww2/p36/p36-2.gif (for P-47 P-36 profile cross-section cutaway comparison)
Also remember the P-39 carried 120 US gal of self-sealing fuel cells in the inboard portion of the wing in spite of also housing 4x .30 cal guns (and capacity for 1000 RPG), so with proper attention to detail (and redesign of the wing ribs to accomodate cells) it should have been fairly easy to expand the P-40's fuel capacity substnatially, possibly while also embedding the radiator (and possibly oil coolers too) in the belly/wing-center section in place of those fuel tanks. (akin to the P-39's radiator and oil cooler core placement) The P-40 also gives a hell of a lot more space for adding a turbocharger than the P-39 does. (especially if compromising to use existing turbochargers aimed at capacities and altitudes perhaps a fair bit beyond the real needs of a fighter for the time -or at least not worth the trade-offs for weight and bulk of the unit AND intercooler installation ... the P-39 might have accomodated a SMALL rear/saddle mounted turbo had they been available)
Finally, aircraft designers (or engine manufacturers) could have taken the lead away from GE by working on liquid cooled intercooler designs rather than those huge air to air ones. (that would definitely make a turbo on the P-40 workable, and probably the P-39 too ... perhaps P-51 as well with the rear tank omitted and some CoG adjustment -remember turbos also mean better fuel consumption and range, particularly at cruise where exhaust thrust is useless anyway)
The P-38 and (especially P-47) would have benefitted somewhat less, but it would have been a far more elegant solution than the chin intercoolers on the P-38, and would have freed up fuselage space for some added fuel capacity in the P-47. (within CoG constraints, of course) Perhaps more significantly, it would have allowed the P-47 to lose much of its 'gut' along with the removal of that large intercooler. (OTOH, using a LIQUID intercooler on a radial engine might be problematic ... unless designed around using oil to cool it rather than water/glycol ... that might have been workable but the viscosity of oil might not promote good flow at the temperatures desired for air intercooling, in any case -oil or water- the radiator would likely be grouped up front with the oil coolers, thus leaving only a small turbocharger impeller air intake scoop needed at the rear -liquid intercoolers also make small targets, unlike the big block in the P-47's rear that could get holes punched in it and lead to a loss of manifold pressure)
The P-51 would NOT have been the aircraft that it was without the liquid intercooler exchange. A conventional air to air cooler (a la F4U/F6F -likely of similar size too, given the mass flow involved) would have added substantially more drag to the P-51 ... or anything using the 2-stage merlin for that matter. (the other option, of course, was no intercooler at all, a la the minimalistic V-1710 Aux stage -and a small number of 2-stage R-1830s for that matter; in which case either VERY high octane fuel was needed for WEP -like 100/150, or water injection had to be employed -which risks corrosion of the engine if used too soon before landing and shut-down -you need to burn off all traces of water and methanol in the system or risk corrosion, particularly to aluminum components in contact with the methanol -steel alloys and cast iron tolerate methanol/water fine, about as well as plain water, but aluminum is not so nice)
