I agree, almost! Yes, you should drawfile the entire barrel. If it were my project, I'd then polish backing abrasive cloth with a large flat file starting at 120 grit, and ending at about 320. Polish lengthwise, just like you did when you drawfiled, removing all marks left by the previous regime. then de-grease thoroughly (I use Comet and a Scotchbrithe pad) flush with clean water, dry with paper towel, and handle only by the pegs you've driven into the breech and muzzle. Never touch the barrel after polishing, with your fingers.
While you are de-greasing, prepare your damp box so it's ready to start when you are. Lay the barrel on wooden V blocks by the pegs, to apply the solution. I use a roll of cotton cloth about two inches long and 5/8" in diameter. Dampen the roll and squeeze out the liquid before you apply to the raw steel. Start at one end and apply using even pressure from breech to muzzle only on one flat at a time. Do not go back over areas you've applied solution to. Rotate the barrel one flat at a time until the whole barrel has one even application. Use a Q tip for sight dovetails and around barrel tenons. Be very careful not to let the solution run, even a little. Remember to apply a coat on the muzzle around the peg.
I hang my barrel by screw eyes in the wooden pegs and hooks on the ceiling of my damp box, starting muzzle down. I record the time and apply the next coat in 2 - 3 hrs., alternating hanging from the breech to the muzzle each time. the barrel is not in contact with anything in the box - hangs freely.
After the second app. the barrel should be covered fairly evenly with light brown/red rust. I run it down hard with a roll of canvas cloth about 1 1/2" dia, x 5" long. I use only one end of the roll which gets very rusty coloured but removes all of the loose scale. If you have given your barrel a high polish, ie: 600 - 1200 grit abrasives, you will likely want to card further with 0000 steel wool. After 6 - 8 apps like this, you will have a deep brown colour IN the steel rather than ON it. Without carding you will end up with a coarse rough pebbly brown that may be subject to flaking.
When you are done and satisfied with the colour, and have carded for the last time, take the barrel (by the pegs) to the laundry room sink and pour boiling water ( a full kettle full) down the barrel. This will remove any latent solution and heat the barrel. Then scrub the barrel with a solution of baking soda and water, or with liquid ammonia, to neutalize the acids in the browning solution. Flush with clean water, dry the barrel and apply a sealer like motor oil, floor wax, etc. Allow to cool, remove the pegs, clean the bore immediately in case any water entered around the pegs. Step back and admire the professional, even, lustrous, even brown.
I am assuming all this is new to you, judging by the questions you have asked so far. I intend for this to be positive instruction and not an insult to your experience or intelligence.
Oh, one more thing: if a black/blue is preferable to the brown, before you card it for the last time, boil the barrel in a tank of DISTILLED water for about 20 min - 1/2 hour. Then card using 0000 steel wool or a Brownell's carding wheel.
