Something related to the snap cap diameter and your bore diameter does not seem right. Maybe your bore has been altered. Does the snap cap slip entirely up the barrel to the choke area ?

Why not measure the snap cap diameter , and then measure the bore diameter ? Most German 20 ga bores are fairly tight. Measure the bores just ahead of the chamber, then at 1" intervals going toward the muzzle. I wonder if the gun has had the forcing cones lengthened .