While the Hellcat can turn very well, especially with the aid of a notch or two of flaps, it's heavy, and has poor acceleration. This means that you should try to stay fast if you are facing more than one enemy. The F6F is my second favourite plane, one down from the 38, and the two planes are very similar in that both fall between "average" and "good" in most characteristics, but hold few to no trump cards, so it's all about being aware of the strength and weaknesses of your own plane and the planes of your enemies, and applying them appropriately.
In the F6F, your strengths are:
-Above average instantaneous turn rate at all speeds
-Low stall speed and good sustained turn, especially with use of flaps and rudder
-Good dive handling and acceleration, remains controllable at very high speed
-Good zoom climb due to heavy airframe
-High durability
-Good view over the nose for gunnery
Your weaknesses are:
-Mediocre top speed
-Poor level acceleration
-Poor energy retention
-Fairly crappy roll rate at low speed
Against an LA-7 you definitely want to try to force them to slow down and fall prey to your superior stallfighting characteristics. However, against multiple opponents, the F6F will have a very hard time extricating itself from a situation where it gets low and slow, due to the bad acceleration, especially from 100 to 200 mph. So, against multiple cons or planes that can out-turn you, it's a better idea to try to take advantage of your dive and zoom climb to do what I like to call "micro-BnZ", where you perform a series of tight/steep, looping BnZ passes on people, never getting more than 4000-5000 feet above them. You can dive away from most planes, and often it's your only option for building speed, so keeping some altitude is essential.
Edit: Didn't notice the specific situation where the LA-7 is on your six. Your only option is to dump some speed and force the overshoot. Chop your throttle, pop out some flaps if possible, and pull into a rolling scissors. Hopefully you'll have a shot when he comes out the other side. The Hellcat's durability is a benefit that you really feel here, as you have a pretty good chance at surviving a few 20mm hits.