Sorry for not responding earlier. It was getting late and I had to get some sleep.

I've done some independent chip model calculations. The calculations below assume that you think the ICM is a good approximation of the dollar value of your stack. I do.

If you fold, you're still 67% to win a ticket.
If you push and win, you'll be 89% to win a ticket.

Your expectation - if you push and get called - is
EV = (probability to win) * .89 - .67

If we want to find the probability to win where we break even, we set EV = 0. Then rearrange the equation to
Probability to win = .67 / .89 = .75

So you need to be 75% to win to break even. And you're not. So you should fold. Of course this discounts the chance that I would have folded or that I held a lower PP. So it's probably very close. But it's not an easy push. I think I'd call and push on a non-ace board myself.

Another thing you could argue is that I (as the big stack) should keep out of hands like this too. I almost gain nothing since I'm about 96% to win a ticket. But I almost lose nothing as well, when I lose. I'd go from 96% to win a ticket to 87%. The person that really wins in this hand is the short stack who wins about half a ticket.