I do something similar. I usually take the plug out right away while the gun is still warm. I put the breech plug and the striker in an aspirin bottle with Dawn dishwashing detergent and hot water. When I am done with the rest of the gun the fowling on the breech plug and striker come off very easy. I use a tooth brush and a small bottle cleaning brush. I usually use my thumbnail and a piece of a paper towel and make sure the threads are spotless. This works well with triple 7, pyrodex, and black powder. The only powder I have had trouble with getting these parts clean is Blackhorn 209.
I cut and rounded off the edges of a piece of walnut and use that to clean the shoulder of the reciever that the breechplug tightens up against. I usually clean the threads with the brush and then put a patch over this little piece of wood and clean that shoulder.
Works for me anyway
Art