I used an empty .22LR case as a dipper (Bullseye, IIRC) to load some mouse phart loads for my 30-06 using 32 cal pistol wadcutters. I don't recall measuring them, but they might have been sized to .309.
A sizing die for a Lyman/Star/RCBS lubrisizier might solve your dilemma.
Edit: A .313 lead bullet in a .311 bore would not scare me off. A test might be in order.
A sizing die for a Lyman/Star/RCBS lubrisizier might solve your dilemma.
Edit: A .313 lead bullet in a .311 bore would not scare me off. A test might be in order.