I've never heard Hartford's version, but there's one in Irwin Silber's "Songs of the Civil War" complete with music and additional verses.

Wayne Erbsen recorded it on his album "Ballads and Songs of the Civil War." You can hear a sample:

http://www.nativeground.com/MP3s/SouthernSoldier.mp3

The CD (or just the song) is easy to get online.