I read somewhere that the 7.7 indicated the J-bore of .318, which along with the 8-88 (aka 8mm M/88?) marking and the 57 led me to assume an 8x57JR rimmed Mauser chambering.

But I reaaaaally don't know much. I sure hope it's not something that's too weird to find brass for. I passed over a lower-priced drilling in 8x72r Sauer, but that brass would have been easier to find than the 8x57/360. Doh.