Greetings! Good to see you both back in action. I try to keep up still and collect pieces of the puzzle, although I have admittedly fallen behind. Feel free to send me an email if you would like to discuss something in particular, I have a little bit of time on my hands now, and will be happy to help.
Anyway, as to John W. Alberty, I would agree with Ken's observations. On the subject of John Miller's Company, he probably also for a time served in Well's Texas Battalion (July 1863 onwards). Interestingly, the company he led there was formerly W. H. Witt's Company, originally organized for the 18th Texas Cavalry. See https://www.tshaonline.org/handbook/entries/wellss-texas-battalion
I would assume it was Capt Miller who was moved around, and not any of his men, but it might be interesting to compare the rosters of Witt's Company and Miller's in Bryan's Special Service Battalion nonetheless.