It seems like some of you are working too hard cleaning your shotguns. Here is what I like to do.
Take the barrel off and put the wood and any painted parts a few feet away. Take a can of brake cleaner and hose the barrel out, I like to step just outside and do this as the fumes are nasty. When it looks like there are scales growing in the forcing cone area of the bore shoot it out again. The brake cleaner will eat the plastic wad residue right out of the barrel. Same for chokes, 1 minute to perfectly clean. It may take a whole minute in between sprayings of the bore, but not over. The brake cleaner won't hurt blueing or parked finishes, but it will wreck a stock or paint. If you have a factory camo finish DO NOT DO THIS, it will be damaged so back to the old brush you go. The bore is now cleaned of all plastic. You may need to push a patch or two through to get the rest of the powder fouling, but there won't be much. Run an oiled mop through the bore, and wipe down the outside. Wipe out the receiver and oil bolt rails if necessary. Put it back together and you are done. Cleaning a barrel should not take more than a minute and a half, and I regularly shoot several thousand rounds between cleanings. I usually just oil and put it away, clean when the plastic starts getting heavy. Every couple of quick cleanings I will go ahead and strip the gun all the way down and clean it out really well. For this use a can of electronic contact cleaner, hose out the trigger group and the areas of the receiver that are hard to get to. The contact cleaner will not harm the plastic parts (check the label to be 100%sure, but almost all of it is plastic safe) that are very common in trigger groups of modern shotguns. It also will not harm factory camo finishes, most if not all gun specific cleaners will trash the camo. I can clean an 1100 to sparkling clean in less than 10 minutes, a double in less than that.
If you must use a bore brush chuck a cleaning rod in a cordless variable speed drill and run it back and forth while running at a low speed. Two passes and all the gunk is ready to be pushed out. Store the mops in the plastic cases they came in, one dirty to push out the gunk and one clean to oil the bore. Wrap a patch around the dirty mop for the second pass down and back to clean before oiling. Works for me, hope it helps someone.