So, with the Way Hospital Register for J. Bowser 29 Tenn. Inf. Co. K dated February 4, 1865....it be would be more reasonable to think he was with his company at Nashville in December 1864 and made the southward escape from Nashville as you described, and then deserted to Union forces sometime after being discahrged from the hospital at Meridian?
The last company muster roll he was shown "Present" was dated Jan & Feb 1864........a big gap to fill between then and February 4, 1865.
Barry