In order to secure the preliminary injunction, Zeke must show: (i) irreparable harm; (ii) either (a) a likelihood of success on the merits, or (b) sufficiently serious questions going to the merits of his claim to make them fair ground for litigation, plus a balance of the hardships tipping decidedly in favor of the moving party; and (iii) that a preliminary injunction is in the public interest.
As you suggest, Failla completely dropped the ball on irreparable harm. Every court other than hers had previously found irreparable harm in similar circumstances (for example, the Brady case).
But I think she was only slightly less sloppy on [ii] and [iii]. Brady II clearly left open the possibility that the fundamental fairness standard of review should apply to arbitration rulings under the LMRA (which is applicable to this case). Failla attempted to debunk that notion in her reasons, but the fact remains that it is a "sufficiently serious question going to the merits" of Zeke's claim to make it fair ground for litigation. And it's not the sort of question that Failla should have tried to address outside of the actual litigation and as part of a mere motion for a PI, based on limited submissions and oral argument (in fact, that was irresponsible of her, I think most lawyers would agree). Based on this, and the fact that the balance of hardships tips decidedly in Zeke's favor (Failla found otherwise only because she rejected Zeke's irreparable harm argument), I think branch [ii] of the test can be satisfied.
Public interest arguments are always a bit loosey-goosey, so I guess branch [iii] could go either way, but again, these sorts of PIs are habitually granted in similar cases (including Brady) so I assume Zeke will rely on the same sorts of arguments that have held sway with courts in the past.
All to say that I don't think the challenge confronting Zeke is nearly as daunting as Wallach may have suggested.