While Wayne Erbsen and Bobby Horton (the usual suspects) have nice renditions of the song, and other versions can be heard by the the 97th Regimental String Band and Jim Taylor (whose version closely matches the version in the DT), my favorite version I've found of the song is by the band Lonesome Ride. Gary G. Smith, their lead singer, sang it in a simple and straightforward way, without accompaniment from instrumental backing. I bought their CD (Crossing the Wall) and the booklet which accompanies it, but unfortunately neither gave much insight into their arrangement of the song, though the lyrics were substantially a shorter version of the ones you provided above.

You and most older sources cite the song as from M. B. Smith, but a few sources I've found (such as here and here - though this link also talks some about the song's history) link the song to an M. G. Smith -- probably the derivative of a typo somewhere down the line.

The attribution to Smith seems more likely to me. There is a known soldier to that name in the 2nd Regiment, Texas Infantry, Co. C (link) - he was a private throughout his known enlistment.

Further, M. B. Smith seems to have been quite the lyricist, writing this song, The Frontier Ranger, The Glorious January 1, 1863, Hard Times, and probably other songs.

Regarding this song, I found a reference from 1887 which gives as its citation the singing of a Confederate prisoner in 1864, which can be found in The Girard Press, June 18th, 1887, p. 1.

After reading several early copies of the song, the DT lyrics seem to be a modern modification of the song, with the father-fighting elements added in later for dramatic effect.