Vic,
As promised, I checked the headsize. It seems the 9X71 Peterlongo headsize is also a little smaller than 8x57.This makes the 9.3X74R headsize almost perfect for the 9X71.It(COW)shows the rim as being 1 or 2 thousanths larger than the headsize, but this is within manufacturing tolerances an not enough to make the cartridge rimmed or even simi-rimmed. It is a rimless cartridge. It's great that you have a line on a lathe, let me know if I can help you.
Mike