Kind of interesting to shove (but only given this exact board and your hand). 

I'd def check flop, but as played you also block Qx so I guess call if he can bluff with enough hands here (which seems v quesiotable). I hate shoving. 

How likely do you think he is to flat the turn with KQ? Does he have all of the KQo hands here? If the blinds aren't very squeeze happy, he might flat with that hand a lot. He is also likely to have quite a few combos of Adxd as well. QsTs, KsTs make sense. KsTs can't be 100% turning itself into a bluff. And if he is auto turning hands into bluffs, some of them beat you! I like a check fold here on the river as played. I much prefer a flop check. I think the turn lead is debatable.

What hands will he very often turn into a bluff that you beat? Ts9s, 7s8s I'd presume. What else are we auto turning into a bluff here? Obviously any hand potentially, but how many are you almost always turning into a bluff? I can think of only those two hands that I would 100% of the time bluff with.

If you hadn't have bet the turn, I would've liked a river check-raise, possibly even on the turn (but that seems kind of silly).  Whatever you do, I don't think the BTN should be able to value-bet Qx here, and certainly not any worse.  That would lean towards raise or fold, so probably fold. 

I think on this specific run out it's so hard for him to show up with bluffs (even if he's turning some pairs into bluffs) that we just happily fold an "exploitable" amount on this river.  We could do a CRev sim to figure out exactly how wide he needs to be peeling all streets to show up here with enough bluffs that we can fold, but I don't think it's really necessary.  In practice I think it's a clear fold.