Your grandmother may have been providing us with more insight on the organizations and how they describe themselves. The men of Bryan's Battlion would have continued to identify themselves with that unit -- their companies appear to have stayed relatively intact. I believe you mentioned the "3rd Battalion" which fits. The first two battalions making up Col. Stand Watie's 1st Cherokee Mounted Volunteers and then Bryan's (often misspelled Bryant's) being the third Cherokee battalion. BTW, Lars knows the organizations in Indian Territory and particularly Cherokee organizations as well or better than anyone.