Your solution is mostly correct, except for the Dremel part...
Index the breech plug. You can score a line from the bottom flat of the barrel onto the bottom of the breech plug lug.
Remove the breech plug, which may take a fair amount of force. Pad your vise with wood blocks or some such, otherwise you will score the barrel being held in the vise.
Please don't use a Dremel, unless you happen to be the best Dremeler (not really a word..) in the world. Dremel tool is the quickest way to do a bad job quickly!
Just use a file and work slowly so you don't file the rifling. You could use a needle file with a rounded surface, or a chain saw sharpening file or any sort of round file you have.
Cheers,
Norm