Given he 4bets re-steal with such a high frequency his range will be pretty weak here. I would personally 5-Bet him decent size and expect to take down the pot majority of the time. There's enough dead money in the pot already and taking it down without seeing a flop seems pretty good plan. If he calls, the times when he actually has a good hand, pot is going to be small SPR on the flop and you're decisions will be simpler. You'll shove any top pair and flush draws. Also balances your 5-bet range and you'll get ton more action whenever you have KK and AA.
Calling 4-bet puts you in an awkward spot. You will miss the flop with AQ 2/3 of the time and by calling his 4bet you're giving him both initiative and position edge. When you both miss the flop, he will bet and you'd have to pretty much fold.
As for your postflop play, I think it was pretty solid. He's got ton of Aces in his range, since he would elect to 4bet light with blockers in his hand. He checks the turn to pot control and go to a cheap showdown and I would bet the river to get value from his weak aces.