John -- the 2nd (Slemons') Arkansas Cavalry, although designated as a regiment, was actually a battalion-sized command of 8 companies from 1862 to 1864. In June 1864 it was finally recruited to 10 full companies with the addition of Companies I and K. However, no muster rolls from this period can be found, so a full list of men of Co. I is unavailable.
While I am unwilling to state this categorically yet, my research seems to point to the probability that Co. I was the "Ashley Rangers", which had been attached to the 13th Battalion Louisiana Partisan Rangers as Co. A. I'm pretty sure that further research is going to confirm this, but right now the jury's still out. Many of the officers you cited were associated with this command.