I used a rod and brush and push most of the gunk out in plugs. Once free of most of the cosmo, I then used solvents with the brush. I often use gasoline outside and a coffee can and flush/scrub/flush the bore with gas until its shiny and clean. Boiling hot water and a light oiling will complete the cleaning.
As above, removeing cosmo or just for routine cleaning, doing so with Boiling water is the best, cheapest and surest way to keep a barrel rust free. It will do a fine job for non corrosive ammo use as well. It works by dissolving the salts, as water does, and the heat will remove all the water as steam. I pour it from a kettle into the chamber, scrub, flush again, scrub, flush and shake the extra water off, then prop against a wall and let the steam out, and the heat cool off....Then a bit of solvent and patches, than a light oiling and your good to go.
Treat the chamber with chamber brush, or a 20 gauge brush, and be sure to get all the cosmo outta the chamber. If you dont, you can have issues with sticking cases.
I take the action outta the wood and I apply spare cosmo to the metal thats under the wood, barrel and action if it dosent have it.