350 bbs deep with ante

 I raise utg, nitty tag with 13% overall 3bet 3bets btn I 4bet he calls 2x pot left on Q96r flop, I have AA79+ 2 backdoor flushdraws, I pot called, any other option that doesn't suck? What do you do with 4567 here? I thought about betting small with aces since we can pot call so many turn cards but it does suck that we give odds to JT67 stuff and pot gets a little awkward, but I'm guessing that shouldn't be a problem since a good chunk of ours hands contain Q9JT stuff that smash this..