Jim,
As far as I know, there is not a rimmed version of the 9x56 MS Mod. 1905. This cartridge was introduced with and for the Mod. 1905 Mannlicher Schoenauer which requires a rimless cartridge. The 9x57R was introduced about the same time and was popular enough to answer the demand for such a cartridge in break open guns. The 9x57R is the nominal designation( name). The case length is not listed in Dixon ( European Sporting Cartridges) as a full 57mm long, rather 56.64mm. This isn't much different than 57mm and unless the chamber is measured again, there is no way to know now if a piece of swarf or something kept the 57mm gauge out but allowed the 56mm gauge in. The tables in the back of Wiederladen(a German handloading manual by Dynamit Nobel) lists the bullet diameter as 9.08mm( about .357"), but most barrels "slug" about .358", but not all. Most people use .358" bullets, both American and German, with complete satisfaction. If a .358" bullet will enter the neck of an unsized case, fired in that chamber, it can be used. If it will not enter, in your case, trim the case to 56mm and try again. If that works, trim all the cases to 56mm and load as usual. If you are a member of the German Gun Collectors Assn., there is an article about the 9x57/9x57R cartridge is one of the later WAIDMANNSHEILs( one of the GGCA publications). Reprints are available. If you are not a member, I suggest you look into it, you seem interested.
Mike