Thornrose Cemetery records show a "J.M. Johnson" who died Sept 29th 1862 who was with the 29th GA Co. A. I know this regiment doesn't match what you show but its close enough to look into. The date would seem to line up pretty well. I would suggest checking to see if there was a J.M. Johnson with the 29th and going from there.
With old records, you always have to broaden your search out for "close" possibilities - makes it fun. Good luck!