Hi Steve

I look forward to seeing the details of your gun.
For pinfire cartridges to work with this gun, the firing pins would have to protude out from the back side (the case head) of the cartridge case, not from the rim and those dovetail features would need to be replaced with parts that would need to have clearance for the firing pins.
I've seen percussion type conversion cartridges for pinfire system, but with these barrels, every pinfire cartridge I've ever seen or handled would/could not breech up in this gun.

There is provision for a ramrod, although it is missing. I'll measure it's ways tomorrow.

Also this gun has no cartridge trap, the buttplate is solid.

Does your Beringer feature the assisted opening stud?

Note the serial number on these locks.
Is it lower or higher (or not even similar) than the number of your gun?
Are these locks similar to the locks in your gun?
The hammer spindles here are hexagonal fwiw.