Big Stack Bubble Play

I'm significant big stack (I think ~4k) on the bubble in the SB. Blinds are 150/300 and the short stack is on the BB with less than 2 BB, so he's pretty likely to be all in if he doesn't expect one of the midstacks to beat him to it on this hand. The button (with about 2k) minraises. If I had 2k or so, this'd be an instacall for me with any 2--to give myself a better shot at 3rd.

With 40% of the chips, I'm considering everything here tho. If my cards suck, I could fold, as I'm essentially guaranteed 3rd or better no matter what happens, so EV and cEV are almost the same to me--and this is a bad spot, where button's range IMHO is very broad and I'm OOP in a covered pot with someone I don't trust to know not to bluff.

I could call with any two and try and check it down unless the board hits me really well. If the button knows that he shouldn't bet unless he hits well, I think I should call with any two as pot odds are slightly better than 3:1.

After I played the hand, I realized I could've made a fancy play here with any two... I could push. Short stack's pretty likely to fold here, hoping the button calls and he gets a decent shot of sneaking into the money. Then, the button is likely to fold just to wait out the short stack. I think the main reason that this play is powerful is that button expects me to call and try and take out the short stack, so he doesn't need as strong a holding as usual to have raised, and he thinks I have a very strong holding if I raise.

In the actual hand, I folded my T2s. I think that was probably the right play because in $5 + .5, I've decided to stop making any plays that assume my opponents will play rationally. Turned out the short stack beat button's K9 with T9, and I would've won with a boat. But, I went on to win anyway.

So, my questions are: 1) did I play right? 2) do the higher stakes 2+2ers ever make the push play, or am I missing something that makes it dumb? I think the main thing to worry about is the short stack calling, because then the button can call too pretty easily because he'd have to have the third best to finish OoTM.