Col. Grierson is a well-known yankee cavalryman who led a raid from Memphis to Baton Rouge, and was portrayed by the venerable John Wayne in the 1959 release "The Horse Soldiers",the premier of which I saw in N.O., LA. The movie also featured Wm. Holden and Constance Towers. Grierson had his butt handed to him by one Nathan Bedford Forrest at a battle at Brice's Crossroads in north Mississippi-but no one portrayed that in the movie.
I have measured both cartridge casings, the first one found at Camp Moore, a Confederate training camp in S.E. LA, bearing a "U" in the base (union ammunition co., I believe), and my partner found 2 more similarly marked. Our southern boys had no such repeating rifles with brass cartridges. These casings measure15 mm at the base, 26 or 27 mm in length, and are either .44 or .45 caliber (15 mm by caliper measurement, see photo attached).
The second casing does not have the "U" and could have been manufactured by another contractor. These were certainly Union cavalry from one or two different units. The second one was found in south MS, just 1/2 mile north of the LA border, above Bogalusa, LA.