I cannot find any Thos Graves other than the one you mentioned and the one in Co D 3rd Ark Cav CS that enlisted at Pittmans Ferry in 1861 and was dropped as absent in 1863. THis was a Pulaski Co unit which was adjacent to Saline Co and some Saline Co men did enlist in Pulaski Co units, so possible it could be him but no other info is given as to his age etc to confirm.

Giles, after release from prison, rejoined 11/17th Ark Inf Mtd in Co A but deserted in July 1863 and as you stated joined Co H 4th Ark Cav US in 1864 and later 2nd MO Artillery.

I find that John and William who both enlisted at Perry County AR in Co C 3rd Ark Cav US are probably your relatives. I tend to lean more towards them being in Co D 37th Ark INf as possible conscripts. I cannot find a Thomas Graves in any US ARk unit to confirm that he died at St. Louis. Do you have any more documentation on him in the US service?