5/10, stacks 3500

villain limps EP, hero makes it $40 BTN AQhh.  BB and villain call.

flop QsTh7h.  check check, hero bets $80, bb calls, villain CR $280.  hero calls.  BB folds.

turn Ad.  villain checks, hero bets $400, villain CR $1100.  hero calls.

river 9c.  villain shoves $2000.

hero????

villain is a very successful and wealthy mid-age white man with family.  He is a poker enthusiast and tries his best to win, although he has glaring leaks.  Even though he's not a complete LAGTARD he can definitely get out of line from time to time.  He can be over aggressive once in a while (both PF and post flop) and likes to open pots and see flops.  He rarely folds to big 3-bets and peels flops pretty light.  He gets a thrill at trying to outplay young pros, but I wouldn't consider him a whale that just dumps cash day after day.  He suffers from chronic case of FPS and tilt.  He can play his draws both passively and aggressively, depending on his mood.

Because of our stack depth of 350bbs, it would be a spew to 3-bet the flop and play for stacks, even with my seeming strong hand.  I ruled that out.  My question is - can you ever find a call on the river?  My problem with calling the river despite the good pot odds - he CR twice on the flop and the turn.  I have the Ah AND the Qh, ruling out the NFD and the pair+FD.  KJh got there.  the only FD he can have are garbage flush draws.  And even though the villain can get out of line, do you see someone taking this line as a bluff??  And he has to be extremely concerned about me calling huge bets and having less than PSB left on the river.   Alternatively, do you just play for stacks on the turn?  It really seemed like he had KJ or 77 here,