Chuck, most of the Arkansas Post regiments were "detained" and put to work in the Army of Tennessee after being exchanged. Among the Arkansas boys, most of those who returned to this side of the Mississippi were men who were so ill after being paroled, that they were hospitalized at Richmond, Virginia, and, when they had recuperated sufficiently to travel, were given sick furloughs back home. I presume this also applied to most of the Texans, but I really haven't researched them much.
I can't find the specific order at the moment, but somewhere around here I've got a copy of the order assigning the Arkansas Post to the AOT. There was no choice for the soldiers. If they were sick, they came home. If they were able-bodied, they stayed in the AOT.