Hero ~1M, Villain >2M, Blinds 5k/10k/10k button ante

Alex has been playing very aggressively, accumulating a mountain of chips, claiming to have had AA 5 times (he showed it down twice). A few other players at the table are active, entering a lot of pots with marginal hands. Most of them play this hand:

Highly active EP opens for 25k, HJ calls, Villain calls in CO, Button folds, I call 4s5s in SB and BB calls.

Flop Ks7s2d, 135k in the pot

Folds to Villain who stabs 37k. I've seen him stab small bets in position at a number of flops, so I don't think he usually has much of a hand, but raising here seems too risky, since we are so deep and three players behind me are left to act. I call and the other players fold.

Turn Ad, 209k in the pot

Upon turning more outs and also believing that I can represent A2, A7, AK, 22, 77 (I've flat called and shown AK OOP earlier, as well as correctly folding a flopped set), I think leading my 12-out draw here is the correct play.

Maybe my sizing was a bit large because I made it 125k (perhaps 100k is better), but I was surprised that Alex raised me to 360k.

That makes 694k in the pot, 235k to call, and around 800k behind, meaning I could raise another 550k or so.

I tanked long and hard here. After a while I set aside raising because he's getting great odds to call and definitely has me beat at this point, so I have very little if any fold equity and I'll be a 3-to-1 dog to win whereas I need to bet around 800k to win 2M (i.e. only 2.5 to 1).

So is it worth calling to try to hit my outs?

I'm getting close to 3-to-1 absolute odds on the call, plus I could win up to 550k more if I hit. If I know that I have 12 outs then I think I should call (3-to-1 to hit), but can I be sure that I have 12 outs?

My concern was that he could have a better flush draw here, including the As. I was just thinking through whether he could be holding AsXs type hands and make the pre-flop / flop plays that he made when this idiot worst player at the table, not even involved in the hand, called the clock. It is only a 30s clock and the floor came quickly. I didn't have time to figure it out and the clock was counting down...what do you do?

I think you can call here profitably but NOT just focusing on those 12 outs.

Since there are two diamonds as well you can rep a flush draw by calling and jamming any spade or diamond river.
This keeps your play balanced and gives you a range of holdings for both bluffing and value.

If the Ace was a rainbow card where only spade flush was possible I would fold. You're not getting a great price.

I don't think I would be leading the turn here, the ace helps our opponents range more than it does ours. Also I can't think of any value hands in our turn range that we would lead with. Although you said you flat AK pre, this 3b pre sometimes, maybe A7 or A2 but these fold flop often, sets won't usually take this line either. I proly just check and go from there.

I think we have a few dirty outs here, 2s pairs the board and so does the As. If he has a set or AK we could get stacked potentially. Then there is the possibility of him having a better flush draw, all in all it just seems like a really marginal spot to be playing for so many chips, when alot of the time we will just brick river and does he really pay us off 550k if we call turn and jam spade rivers?

as played have to fold