I think folding is correct, but it's close, and very dependant on the bb's playing style.
In my analysis, I use the Sklansky-Peacock tournament equity model, which is explained
here.
First, why should a rational big stack call with a lot of hands here ? Because he has more to gain by busting me than what he has to lose by losing a few of his chips. There is a boundary effect that constitutes an exception to the rule that says that the chip equity curve is concave.
If the bb folds, his $ev is 455$. If he busts me, his $ev goes up to 485$, and if he loses 875 chips, doubling me up, it goes down to 435$. So he gains 30 or he loses 20. This means he only needs a 36.2% winning chance to be correct to put 875 more chips in.
Now, let's look at my position. I did ev calculations by using a hand matchup table, and enumerating all possible weighted matchups.
If I fold, my $ev is 253$.
If I push and the bb calls with anything, my $ev goes down to 174$, even if my Tev goes up.
Now with the set of calling hands that I suggested, which I think is too tight, my $ev is 287$. So in this case pushing is correct, and stays so even if wa account for the small stacks calling with big pairs.
But this is a situation where I'm either a little right or quite wrong, which makes a case for passing.
But this problem is still open until someone computes the Nash equilibrium, using some reasonable assumptions to reduce it to a two player game.