You have all the information on his military service you are going to get if NARA says his were part of the 80% that were burned.What you found is the dates he was promoted to rank and his Units 154th Depot Brigade Company D and 307th American or Ambulance and not sure what Tn is. Looking at 1930 census was your grandfather married after his 22nd birth day and before is 23rd (Nov 29 1917 to Nov 29, 1918)? The one in prison has first married at age 22.
Have you tried the County Library the prison was located or the State Archives?
If you have access try looking up historical newspaper for news item of desertion.