Robert, I will do the easy part first. After the Atlanta Campaign in 1864, Ross' Brigade lead Hood's Army into Tennessee. Their direct Corps Commander was Nathan Bedford Forrest. Ross' Brigade fought for him going into Tennessee and as rear guard leaving Tennessee.
I have found one record that list a G. M. Ellison, PVT, Company H, 3rd Texas Cavalry Regiment. It is all by its self. Next comes George W. Ellison, PVT, Company H, 3rd Texas Cavalry Regiment. George enlisted in Upshire County on June 13, 1861. He then road 135 miles to Dallas for the regimental muster. He was present for duty till 19 September 1862 when he was killed at the Battle of Iuka. George's horse was worth $125 and his gear was worth $25. This could have been a Bowie knife and pistol. There may be two G. M. Ellison records. I was having trouble with Footnote.com records. I will check some more sources. If Meridith Ellison joined or was associated with the unit after the summer of 1863 he could have been a part and only partial records are available. This may be why they mix with Georges. The copier of George's records makes a distinctive W and and the G. M. Ellison is different. I know the initials are not correct, but these are the only Ellisons I have in the Brigade. Many records were reconstructed long after the war, from soldiers memories.

I do think you have the beggining of a link. Will let you know if I find anything else. Click on the link below and then the 3rd Texas Cavalry. You can learn a lot about their unit. Do not get confused by the South Kansas Texas Mounted Volunteers. That was a name they had until they started east to the war.