I've been shooting clays a lot the last few years and therefore doing a lot of barrel cleaning. I have found a quick and easy way that works for me. I make my own cleaning rods out of 7/16 or 1/2 inch hardwood dowel. I put a large slot about 2 inches long at the end so they can hold a large patch or steel wool. The end at the slot is also narrowed or flattened. I spray the barrels with wd-40 and put a large wad of course steel wool on the rod and make about six passes, not letting it go out of the muzzle. I give the choke area, the forcing cone and the first 6-8 inches of the barrel a little extra and that's it. Wipe it out and all the fouling, including the plastic, is gone. Make sure to use the course steel wool. It's soft and won't hurt your barrels. The wd-40 softens the plastic and acts as a lubricant for the steel wool. I can clean a set of barrels in just a few minutes and all of the plastic fouling is gone. And no, I don't use wd-40 anywhere else on my guns.
