Fowler,
My experiences first flying the F6F were the same !!!
I am assuming (from my own experience), the problem is due to the fact that you must be way underspeed (lack of E) and yanking on the stick, will result in the problems you describe. The P-51 will act the same way. You have to have air speed/E (and maybe some flaps) to yank these planes, and in most cases, they still won't out-turn a SPIT.
I would generally categorize the F6F as a "Boom and Zoom" plane and not a "Turn and Burn" plane.
Mind you, there are some "HellCat" and "Pony" drivers out there that can make those planes do amazing things (I am not one of them). I have a squad member that can chew up any plane with his P-51 in either "BnZ' or "TnB" mode.
The F6F needs some decent speed / air flowing over the wings to try to get into the "turn and burn" scenario. Trust me ... if you get the F6F flying within its speed parameters you can do some decent hard turns with or without flaps and can be a very deadly plane with its 6 .50 cals.
If you want to do some yanking (turn and burn) ... try the SPIT Mk IX, but I would recommend that you stick with the F6F and get use to that first. Its a great all-around plane and is great for JABO and then capping an airfield.
Check out this thread ...