I don't really like your min bet here. I understand you are target AK, but when your opponent shows that much aggression in that spot his hand is looking pretty nuttish. AK is now the bottom of your villain's value range, and hands like AQ, QQ, and the one combo of AA make up almost as many combos as AK. Actually, slightly more. 8 AK, vs. 6 AQ + 3 QQ + 1 AA.
I really can't see any bluffs in your opponent's range here. That would be pretty darn tricky to get through.
So even though you do have a full house, as much as it sucks, I think once villain puts in that 4-bet you're better off playing pot control. Call the 4-bet, check call the river, show down, and hope you're against AK. Cause if you're not you're very very likely beat.
The only way this spot favors you is if you think your villain takes Ace hands out of your range with a hand like KK.