Tough spot. You're right that if we call we can't fold postflop any non-ace flop.
Hard to see villain doing this w/QQ or less OOP. Any feel for if villain would do this w/AK?
In retrospect: when deep 3bet KK smaller IP to ~60. If he 4bets this then the pot size doesn't escalate as fast. It's easy to say now but plan ahead as in "if I 3bet to 100 what would I do if he 4bets?"
I think we all know this but in the heat of battle we get excited and most of our thoughts are "I wonder if he'll fold" or "how will I play this when he calls" instead of "what if he 4bets big".
Hard to fold KK here but depending on read I might find a fold this deep