Sucker the k4 into turning with you. If he doesn't hit on a snapshot in the first couple of "threads" on the rolling scissor he's in a tough position. As long as your aim is decent enough to hit him from 400 yds when he either goes up or tries to extend out, the hog super flaps, gun platform, and stall characteristics keep the k4 on a short leash.
F4u's and ki84's are the most difficult planes to fight against in a k4. I could say "it's the plane not the pilot" about most hogs in this match up too. But ultimately it comes down to how the carpenter uses his tools.