assignments. I would just make an officiating assignment to each ward and they forfeit their game unless they provide the officiator for the previous game. I've even been in a stake where they had no officiating and call your own fouls. You would think that would cause problems ... but it didn't. Maybe people dialed down the competitiveness in that situation, I don't know. They still kept score, but we called our own fouls, and somehow it worked. Anyway, I think there can be options.

I would also tell the stake that this is important and they need to make buildings available to you. If the Relief Society can schedule the building to sew quilts, the men should get it for sports. The elder's quorum/high priests budget is minuscule compared to the women, at least let us have the building when needed.