I think they will leap off the heresy cliff. They can't get much smaller anyway. I have no horse in the race but it seems like the American church (Anglican) has become pretty insignificant while others are booming. Do you think they will compromise to keep their buildings or even if they split do they keep the physical assets?
It depends on the state and how the real estate documents were drawn up. They have a good chance in California, a weak chance in Pennsylvania, and a fairly good shot in Virginia.
I've tagged some of the stories with a ' churchproperty ' keyword.