The
Wright R-1820 engine that powers the
Sikorsky H-34 helicopter (and the Boeing B-17) was modified slightly and put on a modified F4 Wildcat at General Motors Eastern Aircraft Division during WW2 to become the FM-2. The
FM-2 Wildcat has less guns (4 vs 6) but more maneuverability and a faster climb rate than the F4F-4 Wildcat. Like the P-47 the Wildcat had a reputation for survivability, bringing it's pilots back after suffering heavy damage. The question is how well does the FM-2 compare to the Jug in a dogfight? Both were renown for ground attack using strafing, bombing and rocket attack.
The training of the pilots has to be considered also. The pilots of the P-47 are part of the elite that is trusted to be pilots or have used influence to become pilots, not necessarily the best pilots available. Jackson pilots are probably more likely to be assigned and advanced due to flying ability than KFS pilots, on average. However, the KFS probably flies more often than the Republic due to a larger support base and availability of fuel.
It would be an interesting scenario to play out.