I use Birchwood Casey bore foam and spray in directly into the bore from the chamber. The uppers sits, muzzle down, in a plastic garbage can, lined of course, with a plastic bag and paper towels.
After several hours, if not over night, I follow up with patches soaked in Butch's Bore Shine on a brass jag using a Dewey cleaning rod. After about eight to ten paces of BBS, I use patches soaked in RemOil to finish the cleaning.
Copper fouling in the AR's and my other rifles, including the rifles that I use in NRA "across the course" matches do not exhibit copper fouling.
I have used this method for over 10 years and have been pleased with the results.