I think this may be a unique time that it's worth it to publicly back the opponent even if there is zero chance of a victory.
This is not a small matter that we don't want to pick a fight over. This is something which we are proud to say is so important that WE CANNOT stand behind you if you impede this, even if you will win. We don't have to apologize or be awkward if you win. We will have no regrets. Because this is an issue that is too important to play politics over.
It may even do more good in the long run. Hochul will see that we are willing to burn our bridges over this, and there is more than political clout on the line for us over here.