Both villains are regs, CO is opening like 40% here and BTN is on the weaker side, flatting a lot of cheese in this spot.

2 folds, CO 21, BTN calls, SB fold, Hero BB AdKsJd8h 87, CO calls, BTN calls.

Flop AcQc7s(264) SPR 3 with CO, 1 with BTN.

Hero?

I did some math and we have a slightly +EV pot/call vs both players, making like 60$ relative to open folding flop, but that's not very meaningful and I'm not convinced that maxes our EV here. It's a flop that the preflop 3bettor should be betting a large chunk of the time, but maybe not all the time. Aside from stuff like total give ups, does this hand that I currently have fit into a checking range?

From a range perspective, betting this hand and folding to a shove from CO is not the end of the world. It's likely OK if we have a small bet/folding range in this spot and this hand seems to fit rather perfectly in it given it's good removal effects but lack of equity to continue vs a shove from CO (assuming we bet like 130 and not pot flop). I did make a simple model of bet/folding half pot vs CO and it did increase our EV by like 9$ compared to pot/call, but I'm not convinced my model is good.

It feel like another option that might be higher EV than both of those is checking, planning to fold vs CO (or call if he bets small), and get it in vs BTN. The majority of the time that it checks around we have a fairly good idea of where we stand: Non T club turns will be the worst ones, we'll likely be able to continue in some way on the other turns. Our equity also gets significantly better than it was on the flop. The biggest issue I run into is quantifying the EV of our checks. There are just so many variables to consider. I can make tons of these generalized qualitative arguments but without a value assigned to them they don't hold much weight to me.

Questions:
1) What is a better way to quantify the EV of checking without having to break down our EV of every possible scenario of flop decisions and our EV on every turn card when it checks through?
2) If you're in the bet or check camp, what is your line of reasoning? Why do you think your choice is better than the alternative?