Fold.
I like pre-flop and flop action and sizing.
Turn check is good. Very tough to get value vs worse with the 4 straight, and you also don't want to build a large pot with your pair. Villain can definitely have 6x and Ax in his range. Ax can in fact be quite a large % of it after limp/calling pre. I expect a lot fewer pocket pair hands (like 77+) because of the limp pre from SB.
Just fold to the river imo. Ax is very possible, two pair like 32, 43 is possible, though I think unlikely since I expect him to be more polarized than that. We really narrowed his range down on the flop and turn to hands that would generally want to get to showdown and hands that beat you. I don't expect him to turn random 5x like 75s into a bluff, and, even so, there aren't many worse made hands to bluff. So he's quite polarized, but in terms of bluffs, maybe a gut shot like 87 is most likely? There isn't much. And problem is, Ax is highly prevalent in his range and combinatorically - say ~A2s-ATs, A6o-ATo = well, not going to do the math, but yes, there'll be something like > 100 Ax combos.
Finally,
Quote:
Is aware he is getting hit in the face by the deck and has repeatedly said it is affecting the way he plays hands.
suggests he will not fold gut shots on the flop. He's getting hit hard by the deck, and it's affecting the way he plays.
The most likely result is that he'll chase longer-odd draws hoping and/or expecting to win.