I think check/push is by far the best play here to be honest.

I don't even know what to put CO on here with his post OOP, check behind a limper, 3-bet a raise from the blinds. But we have a monster on the flop with 12 nut outs, and pushing over a normal bet isn't even an overbet and gives us some FE to boot. Having it checked through is obviously not a concern.