Another good way for cleaning the chamber and lug area is the strip the rifle down to the barreled action, then to place the receiver in a container tall enough to reach over the chamber. Them fill the container with mineral spirits (I use varsol) and let it sit for a bit. After about 15-30min take it out and wash it down with boiling hot water, them do a normal cleaning and oiling. The smaller the diameter of the container the less mineral spirits needed. The mineral spirits will disolve all of the cosmo.
If you really want to do the whole barrel and action, get a 2" x 48" piece of pvc pipe and an end cap and place the barreled action in there (it will be tight). Then add the mineral spirits and repeat the process above.
Best part, you don't have to scrub with a toothbrush and qtips and pipe cleaners.