I don't like a 4bet here with KQo, it might be ahead of his 3bet range but certainly not his 5 bet range.

As played I'd fold the turn and start to think about how to adjust against this guy if you aren't hitting boards. Raising his cbet here might be +EV, i mean its going to look bluffy but he should be folding a lot of his air. I don't think I'd try to get K high to showdown very often...