Bubble, we got AA, and supershortie is sitting out

[Beck]

This is not a hand I played myself, but was posted on a Danish poker forum.
The player gave no reads and no indication of his own image.

On this site, if a sitting-out player is forced all in in the blinds, there is no showdown, he just folds.

This is a 6 man $20 SNG, Blinds 150/300,payout 70/30.
SB (sitting out) 241
BB 4174
Hero 1585
Hero picks up AA. What to do????

According to my own calculations (and please correct me if I'm wrong):
I assume if we fold here, we also fold the following two hands, bringing us heads up, with shortie being automatically eliminated.

Fold (stacks 1135 /4865) ICM equity 37.57
Push and lose ICM equity 0
Push and win (stacks 3320 /91/2589) ICM equity 51.59

Disregarding any FE we have by pushing, are we then able to find our needed win% by FoldEV/WinEV= 37.57/51.59=72.8%
So as long as our hand ranks to win 72.8% against BB's calling range it's a push?

Where did I go wrong?