I expect the church already has a plan. My guess is that it will ultimately abandon civil marriage to the government and perform only temple marriages. The rules will be simple - get your civil marriage at the court then go to the temple for the religious ceremony. I expect church officials will be banned from performing ANY marriages and church buildings cannot be used for ceremonies or receptions of any kind. It will be a sucky arrangement but may be necessary.
I doubt that the method of coping which you suggest would by more than a little time. What is to stop an LGBT couple from going the civil marriage route and then showing up at a temple to demand a church blessing for the same?