More possibilities...
According to Confederate Rifles & Muskets by Murphy and Madaus the State of Tennessee had received 15,087 U.S. Model 1816 or Model 1822 flintlock muskets between 1820 and 1850 under the 1808 Militia Act. Between 1850 and 1860 they received a further 1,033 muskets of the same models that had been altered to percussion and 530 U.S. Model 1855 cadet rifle-muskets.
The same source says that as of July 31, 1861 the Provisional Army of Tennessee (which included the 19th Tennessee) consisted of 22 regiments with a total of 11,955 men, and was armed with flintlock muskets. Presumably those flintlock muskets would be the same U.S. Model 1816/1822 muskets that had been previously received by the State of Tennessee.
The Ordnance Department of the Provisional Army of Tennessee was transferred to the Confederacy in Sept. 1861 and included the facilities at Nashville and Memphis. Both of those facilities were engaged in altering flintlock muskets to percussion and in altering civilian rifles to military use by altering them to percussion and re-boring them to .54 caliber. The number of civilian arms altered was never very large, but it adds another possibility to what could count as a "reconditioned" rifled musket.
As the Confederates retreated out of Tennessee the machinery and personnel from Nashville were relocated to Atlanta, GA and the Memphis works were moved to Columbus, MS. The Army of Tennessee was mainly supplied by the Atlanta Arsenal. Another aspect of the work performed at these arsenals was repair of weapons damaged or captured on the battlefield. A report by Major M.H. Wright for the fiscal year ending 30 June 1863 indicates they had repaired and issued 12,356 muskets and 5,649 rifles and rifle-muskets.
The same source also records that some 4,000 stands-of-arms captured at the battlefields of the Seven Days around Richmond were sent to the Columbus Arsenal for repair. You can see that "reconditioned" arms issued to soldiers in the West could include weapons that were originally captured in the East.
The combination of the words "Confederate Ordnance system" and "reconditioned" opens up an almost endless list of possibilities.