It appears to me the P-43 shows some promise. But you need more engine power without drastically increasing aircraft weight and size.
The R-1830 engne had a decent size displacement of 30L. Can they squeeze another 400 hp from it (1,600 hp total) by thowing money at the R&D department? That should provide plenty of power as long as overall aircraft weight does not rise too much.
Air cooled engines never delivered the same power per liter as liquid cooled engines. You could throw a lot of dollars at the R&D department and not get that result. For your consideration 3 different P&W14 cylinder engines.
R-1830
Take off-1200hp/2700rpm/48in manifold pressure.
Normal (max continuous)-1050hp/2550rpm/7500ft. low gear
1467lbs-single speed supercharger,single stage.
91/98 octane gas
40hp/lt
1.22lb/hp.
R-2000
Take off-1450hp/2700rpm/49.5in manifold pressure.
Normal (max continuous)-1200hp/2550rpm/5000ft. low gear
Normal (max continuous)-1100hp/2550rpm/1400ft. high gear
11595lbs-two speed supercharger,single stage.
100/130 octane gas
44.3hp/lt
1.10lb/hp.
R-2180
Take off-1800hp/2800rpm/unkown manifold pressure. but wet(ADI)
Take off-1650hp/2800rpm/unkown manifold pressure. but dry.
Normal (max continuous)-1300hp/2600rpm/8000ft.
1870lbs-single speed supercharger,single stage.
100/130 octane gas
50,4hp/lt
1.04lb/hp.
The last engine was post war and used the cylinder assembles from a late model R-2800.
As a comparison here are similar numbers for CB series R-2800.
Take off-2500hp/2800rpm/60.8 manifold pressure. but wet(ADI)
Take off-2300hp/2800rpm/60.2 manifold pressure. but dry.
Normal (max continuous)-1900hp/2600rpm/7000ft.
2390lbs-two speed supercharger,single stage.
115/145 octane gas
54.5hp/lt
0.96lb/hp.
For a more fair comparison try using the max continuous power ratings per liter of displacement. This would max cruise or in may cases the power used for climbing. the numbers are 32.8-35.7-36.4 and 41.4 for the R-2800. even the last when multiplied by 30 liters gives 1241hp. If 1600hp was wanted in 1941 it was available from the Wright R-2600 which sort of shows what P&W needed to do, get 33% more power per liter than Wright was getting at the time.
I think the P-40 is a dead end design as it's just too heavy. Things might be different if the U.S. had an engine equivalent to the 1,750 hp DB603 or Jumo 213. And if such an engine would fit in the P-40 without serious weight gain for engine compartment modifications
Whats the point? Both the German engines don't come into play until well after the P-40s " best used by date". Even the R-R Griffon is too late in timing. All three engines are around 500-600lbs heavier than the Allison WITHOUT the bigger prop, radiators, oil system and cowling. With enough redesign it might be done but there would be precious little left of the original P-40 and in 1941-42 when such engines are being promised (but not delivered yet) the P-40 airframe is already 5-6 years old. Why spend time trying to redesign such an old airplane when you could design a new one (Griffon Mustang?)