I think the solution would be simple. If things get so bad that priests are no longer signing marriage licenses for anyone, get married in the church anyway (which is really the marriage that counts anyway) then simply go down to your local courthouse to make it “legal”. Two separate acts in other words.
My wife and I had to do that anyway since we got married in Italy and Italian weddings aren’t recognized as legal marriages here in the US. So we had to go to the courthouse for a seperate “ceremony”. And I certainly don’t regard my marriage any less valid simply because the religious ceremony wasn’t recognized as “legally married” in the US.
It’s the marriage in the eyes of God that counts not the state.
That might be the solution to the issue of the civil benefits of marriage.
But if priests stop signing civil marriage licenses, then there is no longer any pressure on the State to return to defining marriage as between a woman and a man. If we’ve given up on gay “marriage” (which I haven’t done), then I would agree that priest should stop signing civil marriage licenses.
If we’ve given up on gay “marriage”, then I think the next step would be to get the State out of the marriage business altogether and institute a “benefits buddy” system...one that doesn’t require a sexual relationship with another person. Then the term “married” would refer to a church ceremony and the “benefit buddy” would be a legal agreement.