That he served in two units, not three, sounds reasonable to me. You may already be aware of it, but I believe your T. J. Cash is buried in Forest Grove Cemetery in Hapeville, Ga.

As for Tinas J. Cash, I'm inclined to believe that is just illegible handwriting for Thomas J. Cash. There was just one person in Coweta County in the 1860 census named Cash and that was Thomas Cash. But, proving a negative--that there wasn't a Tinas J. Cash--will take more time than I've got.

Good luck with your research.

George