Good news, I guess. I found the source of my trouble - someone with my name with a warrant out in a different state. Different age, but a typo somewhere in the system had me flagged as their guy. It took a lot of phone calls just to find it, and I was glad to find a sheriff's department finally willing to run my name through the system over the phone. It is getting fixed. Now I get to begin the long process of an NICS appeal.

If I find a gun I really want between now and when the appeal goes through, I might try to see if I pass the check, since hopefully I will soon be no longer associated with a faraway felony warrant. But I think that simply having a previous denial is enough to get you denied again.