Very simple.
Install a Napier Sabre VII (Tempest) engine in an F4U-4.
The Napier Sabre engine line was the best Hp/Displacement around at the time.
Napier Sabre VII 3500 Hp, 2238In^3(1) 1.56 Hp/In^3
^ Later models 4000 Hp, 2238In^3 1.78 Hp/In^3
Packard V-1650-7 1419 Hp, 1648In^3 0.86 Hp/In^3
P/W 2800-18 (F4U-4) 2450 Hp, 2804In^3 0.87 Hp/In^3
P/W R-4360 (F2G Super Corsair) 3000 Hp, 4362In^3 0.68 Hp/In^3
^ Later Models 4300 Hp, 4362In^3 0.98 Hp/In^3
R-2800 - 2360Lbs Dry
Sabre V - 2360Lbs Dry (Sabre VII simply had improved internal components so weight should be similar)
You would have a corsair with 550 to 950 extra Hp, with little to no extra weight. The jump between the 1D to -4 was only 450 Hp and took speed from 425 to 448Mph. Add 950Hp! I don't know enough to even guess what the top speed would increase to, not to mention improve on the -4's 3,800 Fpm climb rate.
One issue would be cooling. However, since the P/W had a diameter of 54 inches, and the Sabre was only 46 wide and 36 inches high, a radiator of some could be rigged to the sides and/or top of engine, inside the cowling.
Sorry to get all technical but when I started thinking about this I had to look up data (Momma says I'm "Special"

), and figured I'd share it with y'all.
1.
http://www.hawkertempest.se/NapierSabre1.htm The Sabre VII was similar to the V; the primary difference was the use of ADI and the strengthening of the internal components. From its 2238 cu.in. displacement a phenomenal 3500 hp was achieved at 3850 rpm. Finally, Napier test ran a Sabre at 4000 hp with ADI. No other production aircraft engine has ever equaled these truly impressive numbers !
*Edited: Saw a typo and couldn't NOT fix it.