imho, nobody ever try to date Dreyse sporting guns so I will be the first to do it. I see 3400 now around 1867, next SN in my list is 3437 and also a Lady's rifle in 0,34".
this action was made for rifles and some target pistols maybe between 1865 and 1877 but than replaced with the Dreyse patent action.
think its possible you fill the chamber with so much gunpowder you can get in with the bullet.
6 grain BP was not all in the original cartridge and the big primer pill gave the bullet more energy than every BP load equivalent.
how does it shoot with the undersized lead bullet? better you have a .375 roundball or maybe paper patch the .355 bullet.