I have a sneaking suspicion that every single one of your outs is live. If you think you have SB beat, then a push is looking pretty good. Actually, I think this is a good spot for one of those c-r a-i semi-bluffs I keep hearing about.

EDIT: Cancel that, SB will never fold here. I think you can value bet the river if an A or spade hits, and you can likely c/r if the 2 comes.