I use rubbing alcohol and the brush previously mentioned...I take a patch, wrap it around the brush and slid it in and rotate a few times...Do this about 3-4 times and then dry the same way and lubricate...
Typically, I clean the barrel before removing the breech plug...
Remember the good qualities of that Disc, the trigger is adjustable and I like the convenience of opening the bolt and dropping a disc with the primer in...I hate trying to pick up a 209 primer and inserting it into a hole that's under a scope, too easy to drop it and as I've gotten older, it's just hard to see what you are doing...
When I climb a tree, I take the disc out, then put back in when up and ready to hunt...