Note on the gear:
Don't kick them out for extended periods (there are, of course exceptions). Usually, I'll drop them for a second or so at most if I'm pulling through the down end of a Split-S or any other other nose-low maneuver to keep my speed from building too much, or briefly if I need to slow down quickly to make a last pull for lead and a shot. I really don't use them for forcing overshoots, as the rudder is probably just as effective, and is MUCH faster to clear in order to build your speed back up. The one place I'll use my gear for any extended length of time is in a dive onto a target (either air to air or air to ground) to prevent overspeed and give me more time to line up correctly.
Some other things to keep in mind:
If you can execute it, the rolling scissors works very well for the Corsair because of her high rate of roll.
Use the vertical. It can be argued that the 1-series Hogs come up short in vertical maneuvers against most opponents due to their average, at best, rate of climb (and downright poor as fighters go in the Birdcage) however in my experience the F4U actually has several ADVANTAGES:
The first is her E retention. The F4U WILL keep superior climbers at bay thanks to her wicked zoom (I love watching Ponies and ElGays go vertical with me in the zoom and think they'll either escape or catch me). Advantage in straight climb largely has value on the way TO the fight. Once in combat it's zoom that counts for the most, and VERY few birds can zoom with the Hog. She will also shake off a lot of opponents in a climbing spiral (I've done this reliably against Ki-84s and P-38s).
Second, the F4U can use the vertical (pursuit rolls, high or low yo-yos, etc to keep position on almost any aircraft that will cut inside her in flat turns (especially Spits). If you're tucked in behind a target and he breaks, don't break with him. Pull up vertical, roll to put him at the center of your up or forward-up view, and use that big rudder to haul the nose over and drop yourself back down on his 6.
PRACTICE USING THAT RUDDER. Few aircraft benefit so much from rudder control as does the F4U.
SA is very important for the F4U. Know who is where and in what at all times. Know who can catch you, who you can extend on, who you can turn with, and who will cut inside you.
An F4U with altitude is a VERY dangerous opponent, because they can crank it up very quickly once that big nose is pointed down, and can zoom back up out of reach before most opponents can respond.