Actually, there is an even easier solution. Mrs. Davis is objecting because as county clerk, her signature is required to be on the marriage license, above a statement that says that the marriage is occurring under her authority. To her, that says that she PERSONALLY is giving approval for the people receiving the license to marry. The state could easily change the law removing the requirement that the county clerk's signature be on the license. Or they could change the wording of the license to simply say that the license is being issued pursuant to state law, and remove the language that says that the marriage is taking place under the authority of the county clerk. Either one would resolve this issue.
No. None of them are going to resolve this issue. Our opponents are not practical, pragmatic people who are seeking a solution we disagree with.
They are Jacobins, they are rabid ideologues who want to do to this country and to law what they routinely do to each other.
There is no compromise you can find that will stop them. No sensible solution that will mollify them. No halfway measure that will convince them this far and no farther.
Don't even look for a reasonable solution, because it doesn't exist. Steel yourself to say "no", to stare them down and draw a line in the sand.