I have 6 muzzleloaders with blued barrels and to be honest I have not had the problems with flash rust you are talking about and I clean them in about the same way you do. I do agree that it is important to get rid of all the moisture before oiling. I am guessing a lot of this rusting in your buddies gun was taking place before you got your paws on it.
I have a little mancave with running water to clean my guns in so I don't need to use the kitchen.
Happy New Year to all of you!