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he overbets the pot or makes a big bet he likely has AA.

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Wow, you have very good reads. By just calling his min-raise you don't look like having a real big hands (QQ+ or AK) so when a K hits not an Ace and he has 10s, JJ or QQ, he may give it a try and check fold if you call/raise. Are you saying that if the flop is K23r, and he bets 1500 you fold?

There's 2 options : Call or Push, not a re-raise. If you call, you will have to check fold any non-A or non-K fold. You could also bet 1/2 to 2/3 the pot if you miss to see what he is doing. If you hit your Ace, I would check call, lead the turn and if I hit the K, I would check raise or check/call and lead the turn again.

I am not one of the top players, but this is what I would do.