It's been a while since I got some stick time in a K-4 but here's what I'd do against an F4U (or any other turner). I start by making B&Z passes, but I don't actually intend to get a gun solution. A high energy turner is far too difficult to hit. I only B&Z him to make him expend energy in evading, and I make sure I break off in time to be out of guns range when he turns back into me. I will repeat these fake attacks until he's on the deck, slow and helpless before making the kill pass.
Of course, after a while it becomes extremely boring, which is why it's been a while since I got some stick time in a K-4. It's über, but boring in the long run.