I shoot a lot of BP days at driven birds, normally get through 100+ cartridges.
This is what I do.
Dismantle gun and flush barrels through with cold running water (hosepipe) THEN I mop out with a patch soaked in a solution of ethylene glycol (antifreeze) soluble oil (lathe cutting tool coolant) and paraffin / kerosene.
Use some disposable nitrile gloves = no mess, no fuss,clean barrels.