The La7 in AH2 turns about as well as the Spit 9 does. The Ki-84 turns slightly better (slow), plus it has outstanding low speed handling. The Ki-84 can keep its nose up relatively easily at speeds less than 100 mph, giving you a huge advantage in a low speed rolling scissors type fight.
I've typically found that most La-7s will turn with you until you get close to a firing solution, then they level out and hit the NO2.. I think I'm only like 2-2 against them this tour, in spite of the fact that they are all over the place. I tend to get killed by more nimble planes in the gangbanging type fight your typical La7 driver prefers.
1v1, if you can get one that is willing to fight, I'd say the best bet is to sucker them into a spiral climb, as tight as you can get. Just stay out in front of their guns and spiral upward.. you can keep going up and around while they follow you trying to get guns on you.. they'll stall out before you do. Just make sure you actually do a spiral.. you don't want to be climbing outrageously steep.. they can track you pretty easily doing that.
You have to be pretty quick coming back around though, because as soon as the La-7 stalls the guy will be running. Ideally, you want to come over the top just before he stalls, and shoot him up as he noses down to dive away. You won't get a second chance to kill him.. if the La-7 driver has a quarter of a brain you won't even get a first chance, but the spiral climb has worked on every plane I've tried it on so far.
Also... I'm pretty sure the La-7 out turns the F4U by a pretty significant margin in a sustained turn. The F4U may be able to get inside of a La-7 initially because it bleeds speed so much faster, but once both planes settle into their turns I think the La-7 will turn circles around any F4U.