Bix showed one method.
Shotguns are an Art & Science, that said, too many folks make something difficult, out of something simple.
Take a cleaning rod and chuck it into a battery operated drill. Put on a brush, and add wisps of 0000 steel wool, or finest grit of Scothbrite pad to this brush. Just run this from chamber to muzzle. Leave screw in chokes installed.
I never really worry about a smoothbore. I DO pay attention to the Chamber, where most problems occur. On a 12 ga, I use a 10 brush and do the chamber with 0000 or Scotchbrite. On a 20 ga, I use a 20 ga...etc.
Using one size larger for chamber, also works for the magazine, and the forearm that fits over mag tube.
After the chamber, I concern myself with extraction.
Still the battery drill takes care of the gritty plastic buildup in chamber, the plastic wad build up at choke (my concerns) and naturally the lead or whatever else.
CRC Brakecleaner, if you want to blast all this out. Still shotgun have worked forever, before all these fancey lubes, cleaners and what have you. Please note the conditions these Blued shotguns have been used in forever too, and still are.
Some of this stuff on the market for guns, is the same thing Marketing does for fishermen. 90% of what is marketed is to catch fishermen's wallets, not fish.
Before Battery drills, we did the same thing using elbow grease ( by hand), again the main thing was the chamber. Paper Hulls with wax coating , does better for chambers than these Plastic hulls. It was a snap to keep chambers clean.
Skeet shooters, with tube sets, will run the battery drill between changing tubes.
Some of these guns are quite expensive I might add.