Malta,
I cannot find any "bat turn" in the film.
But I can point out what I think is your major mistake throughout all the film. Energy management.
Every time you look back to see a red icon (almost no matter what the altitude, attitude and speeds involved are) you immediatly get fully defensive and into negative E maneuvering (nose low).
Starting out with the very first merge. Yes, you were in the "worse" situation there - ie you had less E... but going nose level/low to extend only worsened your situation. You were doing right on diving a little to deny him vertical separation, but after that, you shouldve immediatly reversed into him. Your opponent took the opportunity you were giving by extending to get on your high six about 2 K out and started climbing while you were nose low. Also, you were pulling a turn while starting your extension, bleeding even more E.
Later, when you reversed into him, you banked 120 deg and turned into him - right move, but you were doing it full throttle, causing you to speed up even more on the way down. More speed = more Gs = more Energy loss on the reversal. Use your throttle!
You still managed to get him to overshoot, but then either panicked or lost sight (or both) and dove low for ack and the deck.... (E loss!!). You were in the start of a rolling scissor and probably couldve won it (at least you started with an advantage). You gave that up by extending low into ack. Stay with the rolling scissor next time.
The opponent also made a mistake at that point, following you down into ack... and almost paid the price for it.
Right after your snapshot, you follow him in a flat turn (even little nose low). That not only costs you a lot of E, but also increases closure rate and resulting in you overshooting (and getting shot at) in the next turn. Yoyoing off (or at least make a climbing turn and then adjust further maneuvering to your opponents flight path) wouldve been the better option here. Again, E management and closure!!
After the resulting snapshot of your opponent, the next mistake: youre tunring AWAY from him, not only sparing him the possible overshoot but also presenting him even more angle on you. Besides, youre again in a slight nose low flat turn, bleeding off E. Always turn into your opponent - unless you have the opportunity (read: Energy) to run.
Now your opponent finally does the smart thing and extends away from ack (even though he does it at the expense of giving up any advantage. Remember, not long ago, the situation was pretty much reversed... now youre on his six, 2 K out, more or less same E.
Now your opponent reverses into you. (Maybe thats the "bat move" you meant?). I cant check on your film, but id BET he chopped throttle dropping flaps for a second reversing - no problem whatsoever in a F4U at 6K. If you watch his speed and altitude... hes loosing alt, but not speeging up in any considerable way. My guess would be he even was full rudder to help him roll/nose low and also to assist him managing his speed.
You were doing the WORST you could ever do in that situation. Following him down in a SplitS going full throttle. He DID bleed of E pulling that reversal... your opportunity to rope/spiral climb him (watch your opponents second turn and judge his E loss - ie tightness of turn - to decide which one of the "rope options" is the better one).
Think of this moment as a merge. Hes cutting in under you (vertical separation!). You are splitS-ing after him.... nose low, full throttle, speeding up, almost pulling into blackout. If you watch him, he is lead turning you, on his way up. All he has to do is get you into his look up view (lift vector pointed at you) and roll into you.
Again, you were starting to do the right thing (really on the defensive now) and started a break turn. But you missed the opportunity of him overshooting twice (tip: Mouse pointer on gun pipper - any time and any view hes ahead of that, hes overshot) to go vertical ("barrel roll") over and up into behind him. That wouldve left you either with him in your gunsight or at least it a barrel roll with a fighting chance of getting him.
The rest after that is history as they say.
So, wrapping all this up into one sentence: You were too much on the defensive, poor E and throttle management cost you a kill to an opponent that made his share of mistakes.
Another thing i noticed.... you were watching him too little. Youre looging straight ahead, checking where he is every now and then where actually the reverse would be better. Watch him closely and check your own heading every now and then (especially at that ALT, where theres little chance of obstacles in the way).
I know this probably isnt what you were looking for posting this thread, but i still hope it helps you anyway.