I think preflop is usually fine, but it's only really fine if you're not going to be speculating OOP on flops like this. I think c/r flop is way, way better than calling. You don't have enough implied odds to call the flop because villains' ranges aren't strong enough, and it's going to be harder for you to get paid off multiway anyway since turn is going to go check-check-check so often.

When you bink the turn, you need to be aware that its a card that hits both other players a decent amount too, and improves a lot of hands to pair+draw instead of just pair. However, very few of these hands are going to be strong enough to bet the turn with in a 3-way pot (hands like AQ, KT, JT, maybe even AK will check turn), so I don't hate leading the turn. The only problem with it is that we can't ever really be pure bluffing when we do it, so we're relying on villains being fairly clueless about what our actual range is.

Once the turn goes check-bet, though, I think its a 100% mandatory raise. Once AlphaMale checks the turn and you call a bet, he's almost never going to have a hand that can call. Maybe the only candidate is a hand like KT or QT that has a solid pair+open ender, but even then it's probably a bad call in his spot. Your focus should therefore be on getting value from the other villain, who has 2.5k or so behind and a very strong range for betting the turn. I think a small check-raise – small enough that it looks like you could still fold to AlphaMale's shove – would be best here. He's almost never going to fold to it, and he's going to shove over it very often. Once you call, however, you're just risking a card like this coming off on the river – a scare card for a lot of his hands, or a flush card, or a card that pairs the board and either boats him up or counterfeits a 2pair hand.

The problem with leading river is that when you lead river here, you have Tx or a flush, probably 99% of the time. He just can't possibly put any chips into the pot with worse, unless he's really bad. Leading river folds out everything you beat. Checking river isn't great, because he checks back almost always with a lot of his sets and 2pair hands, but you do at least give him the chance to turn a weaker 2pair hand into a bluff or try to valuebet really thin with a set. We're not worried at all about the flush, because he actually more or less needs to have a royal flush in order to have one, unless we think he calls preflop with a lot of weaker Kx suited hands. The only reason the flush card is bad for us is because it makes any potential river lead by us look even stronger, and makes him more likely to fold hands weaker than a straight.

So, in summary, call pre, fold flop, raise turn, check/call river.