A gun of this era stamped as a "13" should have had a bore diameter that would take a .710" gage but not a .729" one. The 13/1 (.719") mark was not introduced until 1887. It has likely been enlarged just a bit. My guess would be the barrel blanks were imported from Belgium & that the single proof is the provisional proof mark. "IF" you intend to fire it make certain he shell used is not longer than the chamber, thus the crimp unfolding into the bore itself. The practise of firing guns with shells slightly longer than the chambers is "Dependant" on the gun having normal forcing cones rather than an abrupt step.
What about it indicates it started life as anything other than a 12 gauge shotgun?
