If he has anything other than KK here I'll tear my arm off and feed it to the dog.

Why have you got a HUD running if you're not going to make use of the information? This is exactly the kind of spot that I use mine for... 4% pfr? I know where I'm at if he 3bets me. My continuing range to his 3bet is simply any pair, I'm set mining with 22-QQ (which means folding on any missed flop, even QQ on a 234 flop) because we're both deep and the implied odds large, and I'm 4betting him pre with KK+. I probably fold AK to this guy pf. At least with 222 I know I'm winning the vast majority of the time, with AK on a Kxx flop I'm still probably losing or chopping at best.

As for getting paid off, well, it got more difficult on the turn. He's either folding his KK or chopping with AK. I'd just shove, occasionally you get a dumbass hero call, and if he folds he doesn't see what you called his 3bet with.