Assuming everyone started w/ 1000 chips (I think that's how Stars work) & the BB has 4000 and the button has 3500, that means the rest of you have less than 1000 each.
I agree with you that your only options here are push or fold. The button raise tells me he has any A, or a pocket pair. The only person he's afraid of right now is the BB. Any other player he can go all in against and come out as the chip leader or still solidly in second with a healthy stack. The other two short stacks are getting ready to face the blinds.
If you're playing to finish ITM (most likely 3rd) then fold and hope the other two short stacks make a mistake facing the blinds.
If you're playing for a better than 3rd finish, or bust, you gotta push and pray.
I've played it both ways and I can't fault either. In your situation with the egg roll where any positive gain is a good one I probably fold.
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