Your gunsmith should be able to make a cast of the bore at the muzzle, using Cerrosafe, a metal which melts at the boiling point of water and shrinks slightly after hardening, then expands to the true dimension after cooling.

Crude, but efficient: if you can find some 8X57JR ammunition (.318" bullets), fire a round and then try to slip a .323" bullet in the mouth of the fired case. If it won't go in, you have a JR, if it will, it's a JRS. A .318" bullet will probably keyhole, if fired in an "S" bore barrel. Conversely, a round of 8X57 JRS will probably not chamber in a .318" barrelled weapon.

Neck clearance is the real problem. With sufficient neck clearance, I am satisfied you could shoot .323" diameter bullets in a .318" bore with no ill effects. Insufficient neck clearance may cause pressures to skyrocket and should be avoided like the plague in any caliber rifle.