"IF the regiment was divided, it would have been along state lines, the Alabama companies being left in this state while those from Mississippi would have been assigned to Armstrong's Brigade of Chalmers' Division."

Yes, this is just how the record indicates they were divided. The four Mississippi companies of the regiment were sent to Chalmer's Division.

I'll see if I have any further information on the mysterious Major Cox. I do know off the top of my head that there were members of the regiment with the last name of Cox. One of them was W.H. Cox, as I recall, who attended a Confederate Reunion somewhere in Arkansas (Little Rock?). No rank given.