I play hands like the LAG all the time. As villian, I would fold to the push unless I had 89s! or Ks. If I had the these hands, I checked to induce a bet and plan to reriase all-in. You

You called two bets, I know you have something you like which includes the As. I check the river and call a reasonable value bet with a straight or small flush. With Qs or Js I bet the river.

You had trouble putting Villain on a range of hands. That is not a good position to be in. I would have reraised the turn representing set afraid of the flush. That way you would know where you stand. As played it looked like you tried to get all your money back in one hand.

I hope it worked out for you.