I just can't agree with that thought process. The only hands you're getting value off of is a few 2 pairs, sets and A(Ks). You can neglect almost all AKs' here because of his weak 2Bet size on the flop. A set is possible but again not very likely at all. These hands are still getting odds to call your 2Bet +EV. If he does have A(Ks), you are never getting action on the river unless he hits. I feel like you played his hand too circumstantially based.
A strong argument for a fold is what does he flat that he shoves to aggression? If KsXs was in the range you put him on here, I think flatting would be best. There's more value to get against your opposition on the river. Does he flat here with a flush less than the nuts? You'd have to know him better to figure that one out, it's very likely he traps any flush here.
As far as ranges goes, his is polarized, but he never has air here, only flushes and maybe a gambling set but it's negligible. I'd put him on [KJs,K10s,K9s,J10s,J9s,109s,J8s,89s,56s].
Given that range, we're getting 2:1 to call before pot odds
, we must. Even eliminating the bottom third of his range, we still get very good odds.
Think of this hand from the villains perspective. 50% of the time he flats your turn raise with the nut flush. That eliminates the possibility of him having the nuts by an even greater amount. But if you were one to have a J high flush or 10 high flush in that spot, you have to make your decision on the 2Bet to shove or fold. Given fold equity it's almost always a shove for me here with The J high flush and a tight spot with the 10 high flush OOP. Your over sized raise on the turn polarizes your range. Had you made it more disable say $2.88 or so, the villain wouldn't likely steal with a 10high flush and would likely 3bet the nut flush as oppose to outright shoving. Given this size it makes things closer, but he's shoving all his flushes here, and for that reason it's a must shove.
Think about it, if you had J10s here would you trap the small stack? Yes.
What would you do if you were 2Bet from the villain? Shove/Fold and likely shove due to all the dead money in the pot. You don't want the spade to run out on the river and devalue your hand. You have to shove this spot and likely be ahead. Your range in his eyes consist of some slow played sets. He's shoving any made flush here.