The reward is not worth the risk. AK, QJ (even QT) and AXdd are all in his range. Maybe JJ or TT for a limp, but probably not QQ.
All true... But on the other hand he also has a ton of Qx, Kx, and other flush or straight draws in his range which are behind. Add to that AJ and AT, maybe even A9, especially the suited combos. JT, too.
Meanwhile, for every JJ and TT , he also has an offsetting 88 and 99, which still have equity but are behind you by a lot; and maybe some KK (though as with QQ he probably would have played those more aggressively pre, though I don’t know the player).
Not to mention all his semi-bluffs and pure bluffs, if he’s capable of either.
On top of that, you still have a few emergency outs (drawing to a boat) with two cards to come. So, even if you’re facing a better made hand, you have a small chance of catching up.
Plus! If he already has a straight or top two, mightn’t he go a little slower to maximize what he can get out of you? Unless he views you as very loose, or is overly afraid of the flushdraw, I’d expect a generic TAG-getting-LAGgy to bet smaller or even check-raise, then get it in on the turn if you just call.
Doing all the exact combinatorix is beyond me here. But in addition to all of the above, since you’ve described him as having become looser as the night wore on, and it's the end of the game, *and* it looks he’s trying desperately to get unstuck, this sounds like a strong call to me.