ITM, there's a tiny stack, #2 stack pushes, SNGPT says call with A4o

I fold this pretty routinely.

Somebody's doing something wrong here (might well be me), but when I plug these numbers into SNGPT, Hero's equity from calling is -3.8% if villain is pushing top 13% (roughly 44+, A5s+, KJs+). Villain has to be pushing something like top 52% to get up to the +0.5% threshold.

If we use the standard ranges in SNGPT and make villain a maniac, hero needs to be calling top 19% (down to about A7o). Tighten villain up to even the loose standard and hero needs 66+/AT+.

FWIW, for BB this is very nearly a call any two situation, and A4o is $+EV against essentially any sane range you could put villain on (+0.9% vs top 13%).

Perhaps this is how OP got the original numbers, accidentally pulling the numbers with BB holding hero's hand?

I still don't see a practical +ev play here. Ok so you are a 52% favorite to win? You win you double your stack but you do not guarantee an ITM. You lose and your out? Will you see this play enough so that the long term odds work out correctly? At the early levels with a healthy chips stack I prefer to play in situations where I am much greater than 50% to win before I stick all my chips in. Pushing with a 52% advantage is much different than calling at 52%. 11's through 55's seem to have the philosophy whoever doubles up first is guaranteed ITM. Unless I have a made hand QQ+ (maybe JJ) I dump it.