I basically do the same thing other then the bore weasel.
Usually since I swab with Windex or there about on the range, I will set the rifle up with the action open and squirt a good amount down the bore and let it run through the bore and out through the ignition system. Then a nice wet patch of Windex and that will force a lot of liquids through the ignition system. Since I shoot a lot of percussion cap inlines, this also cleans the insides of the nipple.
Once in the house I pull the nipple and do basically what you do with the same cleaners. Sometimes I use Simple Green instead of Windex. But at the end, I run dry patches until the bore is bone dry. Then I run a Birchwood Casey Barricade patch through the bore to protect it. Also swabbing about four times.