I can' think of any reads that would change my opinions:
PRE is good.
Flop is good.

Turn can go a couple ways, depending on read on Villain.
Taking the free card is probably what I'd do most often against most villains.

That said, I don't think it can be too bad to bet an A on the turn when the board is 2-pair.
You could get a mid pocket pair to fold, if Villain is capable of folding a mid PP on that board.
It's just that we kinda have to b/f if Villain x/r us, here.

If the turn was a spade, I'd lean more on the b/f or b/c lines, depending on villains bet-size and my read on that.
I'm not looking to get all-in with a flush on a paired board, in general. It'd take a specific read on villain, and I'm still expecting them to show me a full house some of the time.

River fold is fine. You'll be chopping a lot of those calls, and losing plenty often, too.
If Villain was clever enough to b/f his Ax OTR with a full PSB (same as any better hand), then good on him.
Hero sigh-folds and laments it's not all bad when OOP, just mostly bad.