Mark, not too long ago I was reading some Union Army correspondence dating from the capture of Little Rock. As I recall, some of it dealt with the authorization of Unionist home guard or "militia" companies in the counties surrounding Little Rock. I remember Conway County being specifically mentioned, but can't recall the others off the top of my head.
I'll see if I can find that correspondence again, and post it.
As far as I can tell, these companies were never formally mustered into U.S. service, so don't appear in the Compiled Service Records collection.