Appeal. This happened to me in Florida.
It took 3 months to straighten out. Several conversations with the Florida LE folks who run the check told me that if several pieces of information match you are delayed or denied. For example: last name, first name, birthday will get you delayed if these match someone with a felony. All the other information (Social, etc.) will not matter.
So if you have a common name, you are more likely to have problems.
I now live in Virginia, and I just get delayed almost every time. Sometimes for an hour, sometimes for two days.
Good luck, I know you are frustrated and concerned.