Your method is okay for a field cleaning. For a thorough cleaning, take the barrel off, remove the nipple and submerse the breech end in HOT soapy water. Put a wet patch on the jag and run it in and out of the barrel and it will pump the solution in and out through the nipple hole and wash out the flash channel in the breech plug in the process. Run some HOT clean water through the barrel, run a couple dry patches through the bore and let dry for a bit. Run an oily patch down the bore, wipe the outside down with an you favorite rust preventative and reassemble.
The breech plug is removable but not necessary or recommended. It's very tight and the reason you see barrels all scratched up. Seen more than a few with pipe wrench marks.
