The initial designs were, and they corrected this a number of ways like adding weight (armor) to the engine area, moving the MW50 tank from behind the cockpit to the wing*, and some other things like shifting the wing further forward than on the Dora.
All of that basically kept the CoG comparable to other Fw190s (Doras, etc). Much like shifting the ETC rack forward on the A-8s helped counter out the slightly aft CoG. We don't see A-8s tail sliding all over the place in Aces High.
I don't think the P-40s are terribly tail heavy. They're still able to pull off a lot of moves without tail sliding. They did by practice drain their rear most tank first and when you do the same you rarely have problems. Much like our P-51s aux aft fuse tanks. The Ta152, even with almost no fuel in any of the tanks, is still really tail heavy.
* = more to it than that, but the end result benefited the CoG.