Brownells wad solvent and a patch will clean em. Why use something as hard or nearly as hard as your barrel? Only time I use stainless is if I've got a rusty or pitted bore I'm trying to assess. If you're lookin to backbore it can be done quicker with a reamer ;). Don't shoot as many rds as you but my bores that have been nicely polished come clean now with one G96 soaked patch a 10 min wait and then a clean patch, followed by another G96 patch, then a clean patch. I've gone through boxes of shells between cleanings and this still does it.
