Francis D. Allen, 1874, "Allan's Lone Star Ballads, a Collection of Southern Patriotic Songs," contains a number of songs written after defeat. "The Unreconstructed Rebel" is not one of them. The 'Reconstruction' followed defeat, and reached its height a few years after defeat. For this reason, I doubt that the song was written before the 1870s. Authorship by Major Innes Randolph probably is the the best we can do.

I agree with Lighter that the worst versions seem to be from c. 1900, for the reasons he gives.