220-245.
I understand the temptation to flat, but there are compelling reasons not to do so that far outweigh the assumptions being made itt. Flatting may or may not induce a raise from behind, (I think stacks weigh them toward calls) but what is clear is when they DO flat, hero's relative position 4 ways dashes the EV on bad turns with V1 set to stack off in front and V2/3 behind. Even if V1 somehow ck a 2s turn, does hero ck-c, ck-f, bet-c, bet-f?? The equity attached to the Qs will not compensate for any of the big bets to follow outside of pure brick turns.
Another fact, which is bad news is that there are fewer than normal FDs available to V2 and V3, particularly strong ones - this should reasonably weaken V2/3 raising ranges especially considering the action and their stack sizes. Why would even the looser Vs on a 600 stack or a 1300 stack be compelled to semi bluff 76ss when they can flat facing the action in front. Ok, so maybe there are NFDs here as well, but a raise from hero would likely induce more raises from those same stack sizes when V2/3 holds that strong of a draw... A bump to 220-245 should in theory increase heros EV against that set of hands.
Hero should allow V2/3 to make a more expensive calling mistake early in the hand (or ideally a raising mistake) with the small bump, the added bonus of having V1 bet-shove his range after V2/3 mistakes only adds to the play. Naturally, that also part of the plan when hero flats to induce from behind, but the card removal piece (I didn't even mention fewer Qx, fewer 2p hands for v2/3) is enough real evidence to suggest we get too many overcalls that just make turns unplayable and force correct folds/chops with a third of the deck

This is a valid point, but I'm going to go out on a limb here and say that calling is the right answer. There's a very high probability that V3 will pump the action on this flop. If he doesn't, your hand is still disguised.

To everybody getting MUBSy about action-killing turn cards, you're holding 2/8 of the straight cards. If there is more than one call behind, you can safely assume Qx/Kx/AT/AJ. That's a lot of blockers to action-killing cards OTT. You're getting massive action from Qx, since it doesn't look AT ALL like you have AQ. Even in the low chance event that all other villains except the bettor have hands like 98s/T9s/22-99, you're still 70% to see a turn that keeps your hands as the nut hand.

^ Fine. You get another call on the flop.

Turn is a low spade and flop bettor bets 2/3 pot.

Now what?

Wait, back up. What happened OTF? What did the other V's do in this hypothetical?

^ As I mentioned, you got another caller behind you IP.

Btw, I'm just hypothesizing and am not OP.

Depends which of the villains called behind. If V2 called, I'd call again. If V3 called, I'd raise.

EDIT: Renege that. I'd raise in both instances, considering that V1 would be committed at this point.

So you're calling when you have the nuts and raising when the flush comes in? Ummmm.

Oh, my mistake. I honestly misread the board. Thought it was a rainbow flop.

Disregard most of my original post, then.