It seems to me that if they limited their recommendations to only things the entire board could agree on, they could still be productive.

For example, they may not agree on how bathrooms should be organized, but they probably all agree that bathrooms should exist.

The fact that the board had wildly varying opinions is a feature, not a bug. The outputs of this board should be widely agreed upon. If they make declarations that half the country disagrees with, they're going to lose credibility fast. Having an ideologically diverse board helps to secure their credibility.