Although I think that there is a great deal in this, a couple of points deserve mention. Early Confederate strategy was very reactive to Federal initiatives, and problems were addressed in isolation as they arose, and not necessarily solved in accordance with a preconceived theory. Thus McCullough had to go to Richmond to explain his withdrawal from Missouri , so his troops were not scheduled for the east. [Whether they would have gone is another matter!] In November 1862 Secretary Randolph resigned because he was not allowed to order troops from Holmes command to the East. At other times western troops were sought avidly.

Confederate strategy was so erratic that one can ask whether there was ever a policy to either retain or withdraw troops from the Trans-Mississippi at all. Rather such movements were suggested now and then in responce to a temporary crisis.
It may also be doubted if the Federals ever had a consistent policy in the Trans-Mississippi either!
Tony Brown