ligonierbill,
The Danish round was the first one I found but held back for the same concerns you have, especially that it is not a German or Austrian cartridge. It is often difficult to reliably find the nominal cartridge for an old black powder rifle. Everyone was still learning at the beginning of the self contained cartridge era. It seems they left a lot of room for black powder fouling the bullet diameter is almost always smaller than even bore diameter, much less groove diameter( they counted on soft lead bullets "slugging up"). This is compounded by having to compare cartridge dimensions to the chamber dimensions gleaned from chamber casts. Even modern cartridges have to be smaller than the chamber, otherwise they won't enter it. There might be a German cartridge for your rifle, but I haven't found it in Dixon. I often tell people that as long as you can find or make bullets and cases that fit, you can call it what ever you want; you aren't going to ask for the ammo at the "Mall Mart". I guess it is possible the gun was made for a foreign customer.
Mike