You are right; there is a chance that he can get the 2nd circuit to grant a stay. I think it's unlikely, but not impossible. That being said, the NFL doesn't have to prove Zeke was treated fairly; he has to prove that he wasn't. And that's going to be tough to do.
I've posted the link to the Brady decision before, but in it, the 2nd said that the CBA grants Goodell very broad powers, and even if he makes factual or legal mistakes, they can't overturn his decisions, as long as he follows the CBA. Even if the NFLPA can convince the 2nd that Goodell made a mistake in not considering their lead investigator's suggestion, or that he should have interviewed the ex-girlfriend, those are factual/legal mistakes, which they've already said aren't grounds to overturn his decision. The NFLPA would, essentially, have to prove that Goodell didn't consider those things because he had it in for Zeke, and not that he merely made a mistake by not considering them.