The shell stops on the 1200 and 1300 series are riveted in place. If those rivets allow any play, double feeds are inevitable. I have had this happen with a 1200. The only real solution is to replace the shell stop assembly. Better yet replace both left and right assemblies at the same time. These parts are easily replaced without recourse to a gunsmith.
A short term solution is to use the gun as a two shot repeater, then a double feed cannot happen.