4x is fine preflop. I don't really like a 6x opener here.

What kind of range do you think this guy minreraises here? It really affects your decisions in the hand. If I think it means QQ-AA, I'll still play (this may be a mistake, I dunno), but with the intention of check/folding the flop unless I hit it big (like you did). In these situations, TPTP/TPGK carry horrid reverse implied odds though, so you need to be able to play well post-flop.

Flop, I dunno, like I said it depends a lot on what we think his range is. Can we ever move him off KK/AA here?

I'd probably just check to him, and depending on what I think his range is and how he decides to manipulate the pot size, I'd go from there. Suffice it to say that if I thought I could move him off a big hand, I'd be much more likely to c/r or something and if he'd get it all-in with KK here but would still pay me off on later streets when I hit, I'd probably c/c. I suppose for the former example, a bet/push like you did isn't so bad (although with stack sizes as such it's really not an extremely powerful move because he's going to be so pot-struck after any sort of a meaningful raise).