Rim diameter and thickness...
Will a cutdown modern case chamber in this gun?
Typical pinfire cases have very thin and slight rims.

Also, you'll likely need to look at a few different modern hull designs to find one that'll hold enough powder, modern base wads are much taller than the old pinfire cases -- high brass just isn't necessary.
The closest thing I've seen to looking like it'll work is the Activ all-plastic one-piece hulls.
Not glamorous, but very strong and lots of powder room.

Oh, another thing.
Don't load these with the balls touching the rifling. Some jump is actually good. Double rifles typically perform best with some jump.
One thing to consider is how the 'second shot' barrel will do with the recoil. You don't want the second roundball sticking in the rifling before it's fired.
Also a little jump can help keep pressures down.



--Tinker