Hi Nor'Easter,
No, the lid can be loose but the part needs to be packed tightly in the charcoal to prevent air from contacting the metal. I put a layer of wood charcoal first in the box, then pour in bone charcoal. The parts are bedded in the bone charcoal because of the finer grain and greater air exclusion capacity. I add more bone charcoal on top and fill out any residual space with wood charcoal. The top of my box is loose. I buy bone and wood charcoal from Brownells but I believe there are much cheaper sources. I don't recommend making it because it must be very clean burning to get good results. I am familiar with the guns you posted and suspect the barrels were temper (fire) blued. Essentially, they were polished bright, degreased and then placed among nonsmoking and mostly burnt coals in the forge. They were kept in the heat until the blue color emerged, immediately removed and rubbed with oil and emery, then degreasing, and heating again. It was almost like charcoal bluing except the barrel was not completely packed in the coals so the gunsmith could see the color change. A description of this can be found in the book "Espingarda Perfeyta", which is available online. It is a gunsmith manual written by 3 Portuguese brothers at the end of the 17th century and published in 1713. It was translated and republished in the 1980s.
These photos show charcoal bluing on a late flint English rifle I built.
However, when it comes to the barrel, I found a reasonable alternative using rust bluing that looked much like earlier temper and charcoal bluing colors colors. I simply rust blued the barrel (of course it gets immersed in boiling water during that process) and then finally rubbed back the deep blue with Scotch Bright pads to give the color a more translucent appearance like good charcoal and fire bluing.
The secret, as always, is a nicely polished and degreased barrel. The better the surface of the steel, the brighter the colors.
The temper bluing on the locks below was done simply by placing the parts in my heat treating furnace (no charcoal pack) and programming it to heat them to 590-600 degrees for an hour. Again, the appearance is enhanced if the steel is well polished and degreased.
Simple temper bluing looks nice but it does not wear well over time and will eventually fade. Charcoal bluing is much more robust but not nearly as resistant to wear and rust as rust bluing.
dave
dave