Is the fouling is getting in from the front of the cylinder?

First thing to try is to liberally apply a heavy grease to the arbour pin and to the aperture in the cylinder. This might help to keep the crud out.

Not familiar with the exact configuration of this gun: Some have a protrusion at the front of the cylinder where the arbour pin passes through (like a bush proud of the cylinder face), so that the escaping crud from the gap between the chamber mouth and the barrel cannot easily get to the pin. Is there an excessive gap at the very front which is allowing space for crud to get in? Would a thin washer in there help to plug the gap?

Does the cylinder have a lot of fore/aft play when on full cock? (there will be a little)