In the mid-1960s, I saw a very early Ballard that used either rimfire or percussion cap. To fire with a cap, one loaded a RF cartridge that had a hole punched in the center.

Exactly, the Gallagher was similar.
This vid. shows the loading and firing of one. A similar system but without the large rim and more normal chamber, fitting tight to the breech of the bl.
https://www.youtube.com/watch?v=J9_V2gVw5jA&t=340s