Few complete inspection reports are found in the O.R. Those which are have been noted within the microfilm series mentioned previously. Prior to the last year of the war, inspections appears to have sporadic, not occuring on much of a regular basis. However, in 1864 that situation changed substantially for units assigned to Virginia and the Carolinas, which were inspected once monthly. Units in Mississippi, Alabama and Georgia had them less frequently, but even isolated commands such as Roddey's cavalry in North Alabama had at least two inspections, one in July and another in October 1864, the latter just after Forrest's raid in middle Tennessee. Also, newly-created commands such as Ashcraft's Mississippi Cavalry were inspected and reports forwarded to the War Department.
None of these are found in the ORs.
As you noted, Confederate law allowed and even encouraged officers and men to use privately-owned weapons. This practice would have helped the government offset the lack of firearms available for its troops in the field. Military regulations as you noted were designed to shepherd available weapons and keep them in the hands of those actually in camp and field service. You also noted (quite accurately) that the government paid for the use of horses in service, recompensing soldiers for appraised values when animals died or were killed in action.
That being said, I have reviewed several thousand Confederate service files over the years and seen countless examples of payments made for all kind of reasons. In at least one example, an officer defrauded the government by submitting duplicate and even triplicate vouchers for the same item. Payment vouchers for horses killed in action aren't hard to find. However, I have never seen a voucher or payment receipt for a privately-owned weapon used or lost in service.
If anyone knows of a soldier service file in which one may be found, please call it to my attention.