For the sake of argument...
 

In the same situation, how would you play K2s?
I think that's a tough call.

Re: For the sake of argument...
 

Push it. You said BB was tight. This is a really clear push given the desperation that 4x BB brings, especially from the SB.

Hell, even if you flip over your cards, it's still a +Chip EV push, and it might even be a +$EV one.