A couple thoughts here... If you "slug" (better yet, cerosafe) all the old 8x57 "jr" drillings out there, you will find the bore diameter all over the board. Some are so big you can use .323" bullets in them, YET they are not marked as an "S" bore.
As for a cartridge, "If" i was going to use that drilling in the lower 48, i'd pick the 7x65R. For me, it's just about a perfect non DG round, and would work on anything i'd ever hunt with it. Loaded with 150NP's, i'd be a very happy camper...
Personally, i prefer ALL of my break open guns to be chambered for "rimmed" cartridges.
DM