I watched the film and I didn't see any UFO N1K stuff, just a big slow hog getting caught trying to turn with an N1K, then trying to run when it was too late. You had one really good gunpass on the N1K at the beginning, and I think you should have put him away there. In fact I was surprised not to see any damage on him after that, but oh well.

After that, you made a few mistakes and it cost you. You started out with a huge E advantage, but you slowed down more than necessary by turning quickly back toward the N1K after every pass. Watch your speed and the N1K's speed--you'll see your speed advantage diminishes after every pass. It's not futile to use vertical maneuvers against N1Ks, but if your speed is about even and he's on your six, don't even think about going vertical.
edit: ONe more thing, looks like in AH the N1K has the climb speed advantage over the F4U-4 below 8k, which is where this fight occurred.