3b JJ, facing flop c-raise from unknown

I know everyone's gonna hate this answer because omg vulnerable hand get it in or fold! But I would flat here. It is very obvious what cards we don't like (except for Js, which we block half of and gives us redraw outs anyway, and A is a bit of a sigh), and we can get away from those 12 cards while rarely making a mistake. Sure, we lose the chance at his extra $13.70 on any turn T or higher, but the fact that 1) He gets the money in much more on a safe turn then he does to a 3b shove (in itself makes up for much of the value lost on broadways), 2) we save ourselves half our stack on a bad turn, and 3) we get the money with 8%-ish more equity, which translates into a lot of eV.

I'm assuming villain is a fish based on non full stack and cold call of 3-bet. That's enough info to make him something more than an unknown imo. I'd be surprised to see anyone who raises 99-TT A8s etc here fold to a flop jam so think that if we're planning on not folding then flop is the place to get the rest in. 6, T, 9, Q, K, A turns happen frequently and defo hurt us by either improving him (yet it's still a guessing game when he ships, with this much already invested folding is bleh on many of these) or by making him reluctant to stack off with worse. I play the same but I'm not thrilled about it, nevertheless given villain is likely bad I'm not folding JJ here, this is the worst hand I'd felt though.