It is quite right that there is very little published on Peter Hardeman's regiment, or the 1st Texas Cavalry, Arizona Brigade. The best synopsis so far is found in Ralph A. Wooster, LONE STAR REGIMENTS IN GRAY (Eakin Press, Austin, 2002). It devotes a chapter to Gano's brigade in Indian Territory, as well as some background information on the regiments in that brigade.
BTW, William P. Hardeman, brother of Peter, does not appear to have served with this regiment at all, but was the original choice for commander when the regiment was being organized by John R. Baylor. Also, like the editors of Official Records, Sifakis' has mixed up his history of this unit with Hawpe's 31st Texas Cavalry, and lists several field officers in both regiments, including major Mike Looscan, who certainly served with Hardeman's regiment, but not in Hawpe's 31st.