(Disclaimer - I'm by no means the best pilot in AH, just perhaps above average)
But I do fly the Corsair almost exclusively, and it depends. You left 2 important things out of your synopsis - Did he reverse, and which Corsair? Assuming -1A since that's mostly what's flown, if you reversed, and he did not, and he had a significant speed advantage post-merge, then you want to climb away into his six to keep him from zooming up under you - if he lets you that is. The 2 aircraft are so close in speed that any speed advantage means you won't catch him if he straightens out, and while 4 K isn't enough altitude to build speed from best turn rate (about 150) to where the Corsair handles well and the Spit 16 doesn't (somewhere over around 320), if he stayed at near corner speed speed during the merge and is drawing you into a wide left hand spiral at much above 300 then you're dealing with someone who knows how to fly his aircraft very well against yours, and you'd probably end up in his kill bag.
If on the other hand if he's gotten co-E or less with you during the merge, then I'd be inclined to suggest going nose low to no more than Vc and cutting the corner to get onto his six. Once you're on his six he's got real problems, as your aircraft is just as fast, and retains E far better while you jockey for the shot.
What I'm not quite sure of because I haven't yet had (or taken) time to do the appropriate testing is who has the actual advantage if you allow the engagement to devolve to a pure angles fight (circle on the deck), given that the Corsair has maneuvering flaps, and the Spit doesn't. Based upon anecdotal observation of my own sorties it seems to depend on the pilot and/or fuel states in that match up. One problem is that so many of the lesser skilled pilots gravitate to the 16 that when I win one, I can't tell how much was because of the aircraft match up, and how much because I might be getting more from my plane than he is from his, even though his might be more capable.
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