As a part-time gunsmith, I've had really cruddy shotguns brought in for cleaning, even some with rusty bores!
What I recommend for shotguns is to attach a bronze cleaning brush of the proper bore size, but somewhat used, to the first two sections of a three section cleaning rod. Place the other end of the cleaning rod in an electric drill (3/8" variable speed). If you have a padded bench vise, set the barrel in the vise. Place bore cleaner on the brush and work it into the bore, starting from the chamber end, if possible, running the drill at relatively low speed for about two minutes, then add more bore cleaner and continue to run the rod in with the drill operating at moderate speed. If the two sections of rod don't reach full length, do it from each end, if you can. If not, do it from the muzzle end, since that's where the most leading occurs.
After a few minutes, run a snug patch with bore clean on it and check the bore/choke to see how it looks. If it appears clean, run a few more soaked patches through. If the bore still seems fine, run a dry patch through, then one with rust-preventative like Break-Free on it to keep the bore from rusting in storage.
It takes longer to write this than it takes to clean a shotgun with this method.