Surely there’s scope for some creative negotiation here.
Each side has something that the other side wants.
With the common ground thus established, you need a negotiation strategy to get what you want, without conceding too much from the other side.
Start with trying to establish some reasoned communication with the other side.
Look at longer term cost savings - a subject dear to any manager's heart.
And the serious talking is done behind closed doors, not through the media.