I think I'd 3b flop, because this texture doesnt look like a texture where people just raise random 2cards. Most likely he's raising a draw or maybe thin value with a hand like A9.
Turn is an annoying spot for me as I dont exactly know which hands are the best defends after the clear defends, but I think 54s is good, because you unblock bluffs and block a huge part of his flop value raisingrange.
Vs this turn bet, if you call the pot on the river would be 69.5BB, with 65.5BB behind, so villain is basically setting it up for a river shove.
Thought about 3betting the flop as well, as you said, at that point you're still good most of the time, but what range would you be 3betting the flop here in general / how common of a line it is to bet>3bet the flop? Like here you wouldn't be bet>3betting and overpair, unless it doesn't block any possible (BD) draws...? OR is 3betting the flop is rather 'exploitable' / used under some specific circumstances?
Villain shouldn't have 95 94 on the flop, neither 96 65 64 on the turn given his line, but IMO 32s 73s(?) 78 are somewhat possible, so i suppose it's too thin to raise the turn overbet, but you aren't folding the turn (you're hand is better than overpairs in terms of hand-strenght and also blocks sets), are you?
I think 3b flop is better than call. Several reasons.
1- villain is quite likely to XR for value thinly against the 1/3 with hands like A9, FD+OCs. And those get really punished by the 3b.
2- As you said, we have enough equity to stack off flop if villain wants to, since he shouldn't have off suit 2pair.
3- As a general plan, calling flop to raise safe turns is a great idea. I think this situation is not very good for it because there a lot of cards that don't let you do this - clubs, 6, 7, 8 ,9
As played, I think you only have one play: call. I don't think you can jam now that villain has 87o in his range. Unless we can discount it a lot. And the double flush draw really makes me want to jam, but i it's probably too loose/spewy.