With apologies for complicating your search, a "Solomon J. Le Andrews" is recorded in the NARA POW records (M598_74) as having reported for his final parole at Washington, Louisiana on 19 June 1865, being registered on the parole list as a member of Co. K, 4th Engineers (CSA), and being listed as a resident of St.Landry Parish. I think it likely that this is your SJL Andrews - the "Le" being a handwriting error of the Union officer compiling the parole list.
The 4th Confederate Engineers was formed in NW Louisiana late in 1864, or early 1865, from men who were swept up by enrollment officers during the late stages of the war.
If I remember correctly, the 4th LA Cavalry (Bush/Bringier) was redesigned as the 7th LA Cavalry in late 1863, about the same time the 6th LA Cavalry was being formed. I don't believe it was uncommon for men to drop out of one unit and join another, particularly, in order to be serving closer to home and family.
Hope this helps