Ron and I have talked about this a good deal, but at the time of the letters, I believe they were acting as an independent company that was rounding up deserters, etc. There were several independent companies running around SW Mississippi during the mid war, some causing more harm than good, but they were not organized into units until later in the war. I think that the 24th the only official designation that the unit (Capt Miller's Co) may have had.
The events in the letters are definately 1863 dates, so I would 99% rule out typo, thought we don't have the originals (copies) to look at.

Virgil