I think there is really only one sound solution to this problem Since the problem is confined to a single county, let people go elsewhere to get their marriage licenses until the legislature can come back and fix the problem, and let Ms. David sit in jail until then. Do the same with any other county clerks who follow her example -- I doubt that enough will do so to pose more than a minor inconvenience until the state legislature can deal with the issue.
Any other approach would create more problems than it would solve.
The problem Kentucky has is that they gave one person in each county the authority to issue marriage licenses -- and thus the authority to gum up the works at any time for any reason. Does any other U.S. state do that? My guess is that there are a small handful that do so, and the other states with that setup have just been lucky so far.
It's actually pretty common, as I understand it. It's not that there's only one clerk signing forms, it's that the County Clerk in charge of the office refused to let her subordinates do their job.