Was going through the M1281 ordnance returns for June, 1864, and compared what the third and fifth regiments carried. Both of them carried a lot of Elongated Ball Cartridges, Calibre .54, and Elongated Ball Cartridges, Ballards Rifle or Carbine, (metallic.).

The calibre of the Ballard's isn't listed, but the .44 Ballards long could also be used in the Wesson rifle. The fact that the 3rd had Wesson's, and used this ammunition, and the 5th used the same ammunition also points to the Wesson rifle being used.

And yes, I'm compulsive.