Pooch, you are simply trying to make an enclosure where the humidity is high enough to accelerate rusting without getting too humid and allowing condensation to form, which will cause streaking. Alternately, you can just wait until the humidity outside is high enough to rust your barrels, because you can run into problems with an improperly constructed damp box. You can get too warm and humid at one end while the other end cools and permits condensation on the metal.
Boiling after rusting and before carding converts the ferric oxide (red rust) into ferro ferric oxide (black rust). A good rolling boil will give a faster and more complete conversion than simply pouring boiling water over the barrels. A long pipe burner gets this job done much better than a couple burners on the stove. Additional expense, yes, but still much cheaper than a divorce. A stainless boiling tank is nice simply because it will not get all rusty while in storage between uses. A little rust in a regular carbon steel boiling tank won't hurt anything though. But coating it with oil to prevent rust may give you oil contamination problems next time you use it. Any traces of oil in your tanks or left on your barrels wil float on the surface of the water and cause problems.
If you've never tried rust bluing before, I'd advise practicing on some junk barrels until you learn the process. My first attempt years ago was on an H&R 922 revolver. I read all I could find on the process and I used the 1873 Ordnance formula from Angiers which bit a little too hard and gave me a matte finish. No tank or pipe burner needed because it all fit in a large stainless soup kettle. The gun still looks good today, but not glossy-shiny.