I had the same issue with an early Fox Sterlingworth. Very difficult to close when loaded. I took the barrels off and the shells hung up on the rims when the shells were dropped in the chambers. I had some assorted pre-WW II shells and they dropped right in. Modern shells seem to have slightly larger rim diameters. Perhaps to function better in repeaters.

I took the gun to a gunsmith who had the proper rim cutter and he did the job for 30 bucks. Brownells sells the cutter but it's probably cheaper to find a 'smith. This was 12 ga. Fox but I know this is also an issue on early 28 ga. Parkers.