[rwanger]

Don't know if I'd have time to think this up on the fly, but my first instinct is:

I like that you're trying to represent KK again...that being said, he ISN'T going to give you credit for KK no matter what you do, because you just had it. I think if you reraise you are letting him off too easy when you are ahead. From your previous encounter, he probably respects you, and might even be able to let go of an AQ type hand.

Check and call him. Let him think he's ahead. That way, you won't blow him off a worse hand on the flop, he'll probably bet worse hands on the turn (again AQ, etc), and if he's min-raising you with a better hand, in my experience, people who min-raise with sets, don't always bet them aggressively enough to double themselves up when opponent is willing to do so. And you'll save money by check-calling rather than reraising.