I show both of those as two Privates in Company G "Pickens Stars", mostly of Pickens County. My information is just a little different than yours. I do not show them as conscripts. I show J.P. as surviving until the Battle of Atlanta, where he received a wound in the leg. I show J.R. as "John R." My information comes mostly from sources other than the CSR.

COX, J.P. (Enlisted Pickens Co. Captured & paroled at Vicksburg. Severely wounded in leg at Atlanta 7/28/1864.)

COX, John R. (Enlisted in Jefferson Co. Captured & paroled at Vicksburg.)

BTW, that is good information that you have found and provided on the leave after Vicksburg. What I have found was written by the Union side...thinking that moral was so low that the army had to be kept together to keep it from totally dispersing. Evidently, this was based on them leaving as a unit, but not knowing that they were furloughed when closer to home!