[locutus2002]

I'd call and play for set value.
I think a fold is better than a push.

Here's why I don't like a push.

Hero has no ability to fold out the following hands: 88++,Ak,AQ. Roughly 70 hands, 3 opponents, or 210 instances that hero gets called and shown one of these hands. If villain's ranges are about 300-400 hands then you are getting called 45%-55% [1-(70/300)^3 ]of the time by one player if you only consider these hands.

When you get called by these hands your EV is ~12K (-17K EV from your original 29K).
In the best case you fold out all the other hands and win 12K for a net loss of -5K EV.

In the worst case villain calls you down with many hands that have substantial equity against 77 such as JK, etc.

I doubt any of the big stacks are going to feel too squeezed by the push, and more than one call could be likely.