Sooo did we consider what hands the villian would be calling our flop bet with and then x/r the turn whenever the ace hits?
We lose to 57/68/66/88 and what other hands is he really gonna x/r the turn with as a bluff? Would he do this with a hand like 77? 99+? AQ? Nope.

When we shove what hands does he call with that he played this way and we're beating? I genuinely can't think of any.
Folding the turn

I think I'd prefer a check back with AK on the low connected 864 board.

Turn definitely bet. After getting raised I think shoving is the worst option of the 3. If villain is very aggro then call the turn raise and let him put money in on the river. By shoving yourself you force out a lot of his weaker hands and although the board is pretty connected 7x and 5x which you should be most worried about are only a small part of the deck.

If villain isn't super aggro then his turn raising range is likely a lot of 2 pair or better hands. There can be tons on this board including A8 A6 A4 and sets. The fact that a large amount of value hands exist mean that he can bluff sometimes but since he still might be value heavy the correct response is to fold.

This is a spot where some info on villain would really help. I'm on the fence between fold and call turn but I think fold might be better.

^ Basically this.
Check back flop quite a lot unless high F2CB on flop.
B/C can't be awful, but B/S is burninnngggg money.

"Never overestimate the strength of a one pair hand in the face of a turn check/raise".

I check back the flop since no made hand is folding and there aren't a great deal of drawing hands that call an EP open. I check hoping to get value on turn from Ax or Kx hands that hit. If villain hits with QJ or JT so be it. As played though I would check call turn. The ace is a scare card for everything villain calls flop with so again we get little value. We can at least induce bluff/semibluff by checking. Shoving is bad facing the reraise here.

Back to the flop, if villain had high fold to cbet I would probably still check back as they still aren't folding made hands almost ever. If villain had low fold to cbet I would bet knowing there are more unmade hands to get value from.

Not a flop c bet for me unless villain is folding an exploitable amount to allow us to auto profit. We still have the best hand a lot but looking to call blank turns if villain bets doesn't feel great if we check behind.

As played I like the turn bet but am folding this at 10NL everytime. Your hand is pretty well defined by raising from MP then firing twice. It's unlikely villain is bluffing here; he's going to have aces up or better almost always.