Joe --
Units are described as 'Confederate' rather than Georgia or Alabama or some other state when a majority of members represent more than one state. For instance, the 3rd Confederate Cavalry includes officers and men from Alabama, Georgia and Tennessee, and the 10th Confederate Cavalry was formed by uniting a battalion from Alabama with a battalion from Georgia. To my knowledge, there were no conflicts over which state could claim these commands.
You may have missed my post from yesterday giving the numbers transferred from Gibson's Louisiana and Crain's Tennessee Batteries --
http://history-sites.com/mb/cw/alcwmb/index.cgi?noframes;read=24497
The late enlistments at Atlanta and Chattanooga were probably for men who enlisted in cavalry commands. Dent's Battery included a number of men who had lost the use of a horse and were transferred from their cavalry commands due to being dismounted. Apparently unhappy with artillery service, several of these men later deserted.