Allow to send you two more units to be included on your list:
2nd Mississippi Cavalry, Col. James Gordon, were at Iuka and Corinth. (Dunbar, p. 402-403.)
1st Partisan Rangers, later the 7th Cavalry, under Col. Wiilam C. Faulkner, at Corinth only. (Dunbar, p. 396-97.)
All the best,
Tom