Mental game: how to fold second nuts?

We never folding 2nd nuts

You call here? The only consideration for me (which contributed to me calling) is that I may be beating some value because he may overplay lower flushes.

It's a cooler. It's like AA vs KK preflop.

Exactly. That’s why we are calling. Even if his range here is Axss, Qxss with no flushes lower than Q high, when he shoves we have a 50% chance of beating his flush (It’s basically the AKQ toy game at this point). We are getting (with the money already in pot) better than 1:1 odds for the call. We may see Ax here a good bit, but it still is a good call.

We don’t even need villain to have a lower flush half the time. By my math we are calling 154.12BB to win 279.37BB (the final 413.49 pot minus our call amount). That means to break even we must win 154.12/414.49=37.2% of the time. We can lose over 60% and still make profit here. Easy call if villain will take this line with non-nut flushes

I don't think I would play the hand like you did. I would 2.5x or 3x preflop especially if there's guys with loose stats like that and a low 3B %. Then I would just bet the flop rather than going for a check/raise which is what I'm assuming you were doing on the flop. I'm not sure why you wouldn't just bet the flop yourself. I wouldn't really want to get in 200bbs on the flop vs two IP callers who can each have As9s, As8s, As7s, As6s, As5s, As3s (would expect AsQs to 3B preflop).

Following that logic, I would just call the BU raise and not re-raise. If we re-raise our hand is fairly obvious + we opened ourselves up to getting stacked. Now we're stuck in a spot where we have to decide if they are overvaluing a lower flush, button clicking with a set, or just only have the nuts. We played our hand in such a way where we made their range as strong as possible but we still have to call based on our absolute strength and the small % they have worse. To me, the topic title isn't asking the right question - the problem was how we got here in the first place.

Very good point! I had the instinct of thinking that call was stupid after the hand was over, but actually it's marginal and really the more important spot is the check-raise play. But let me probe you here, if I call the BU bet, than villain will raise and what do I do? If I c-bet flop, then villain raises and triple barrels, what do I do? My point, will I not get it anyway with this distribution of hands? And if the distribution is different, then I may get value from BU calling my check-raise with weakish value, or only one ace or such.