An argument can be made that the Problem was behind the firewall. The engine was a given, it produced 1150hp and that was it until it could be further improved.
There is no way in the world that an 8400# airplane can be a successful fighter with an 1150hpTO engine. That's 7.3#/HP. Contemporary Spitfire Vs, 109s and 190s were in the 4.7 to 5.3 range.
Just too heavy to be competitive without a two stage supercharger or a lot more HP and neither were available until much later.
Aircraft gaining weight happened everywhere, not just with P-40. The increase of weight due to the incrase of firepower, protection and strengthening of aircrame was a result of realities of air combat. If the engine power was not improving by same of better rate, people ended up with underperforming aircraft. Check out the Zero 52c - addition of protection and firepower turned the passable fighter into a turkey because the engine power remained the same. Fw 190A - from the fighter with 20+ mph advantage in it's 1st year it turned into underperformer vs. Allied best of late 1943 on. The big gain in power under 2 km was of no help above 6 km, and 190 gained almost 2000 lbs between A2 and A8, clean, along with more drag.
P-40 can solve it's problems with either with far better engines, or with deletion of protection, reduction of armament, and reduction of fuell tankage. The later 3 options are out - nobody needs an aircraft that becames a torch with a dead pilot after receiving a dozen of bullets, with sub-par firepower, and without range required. The option 1 - far better engine - can solve problems much better, yet the P-40 never got that.
We can see that by mid 1941- late 42, the best performing fighters were powered by engines capable for 1150 HP above 18000 and better. The V-1710 in P-40 was making 900 HP there (V-1650-1 was better, 1150 HP). From late 1942 to late 1943, the best fighters have had engine powers of between 1250-1400 HP (smaller ones) and 1850-2000 HP (R-2800 powered fighters) above 18500 ft - the P-40 have had 1000?
The P-40's predecessor was the P-36 that weighed 5700# loaded. I'm sure it needed leakproof tanks and armor plate/glass, 4x.50cal MGs would weigh more than the one .50cal and one .30cal gun and it would need a Prestone cooling system, but that's still a long way from 8400#. My ex-wife didn't gain that much weight.
Switch from a relatively simple radial of a modest displacement to a decent liquid cooled V12 will ad 800-1000 lbs easily. It will also improve streamlining if design shop is half decent, and P-40 was and overall improvement over P-36.
6 HMGs are heavy (470-480 lbs as in P-40s), with heavy ammo. Protected fuel tanks - 400 lbs? 93 lbs of armor. How much for beefing up the structure?
IIRC there was a say that any pound worth of improvement required a pound to be added to the existing structure.
At the end of the day, the gross weight of the clean P-40E and similar was 1000-1200 lbs greater than of the P-40 (no letter - roughly it was P-36 with V-1710), and 500-700 lbs greater than of the P-40B. P-40F was even heavier.