I think you will always get better results if you heat the surface being browned with a torch to the point where water steams off it. I use BC Plum Brown, and heat the work as I am browning it, using q-tips soaked in the solution to brush the stuff on the surface. I have heated up barrels and used Cold Blue on them to get a rich blue/black finish, which is impossible to get doing it " cold ".
You do have to clean the surface of oils before doing this. Now, when the finish looks good, cool the steel with oil. Some of it will burn away, leaving carbon to bond with the surface and giving a darker color. You can always use steel wool to lighten the surface, if it is too dark for you taste. After I oil it to air cool, I hang the parts up to dry and " cure ", with the oil on the acids. Over night, I seem to get a deeper color. I end up browning the surface 3-5 times, heating it each time, and cooling it with oil.
Remove the oil with alcohol or other solvent before starting to brown again. The alcohol will also remove most of the acid from the prior attempt. When its really done, I remove the oil, flush the metal under the faucet, and rub it down with a wet rag. Then take it out into sunlight to get a final look at the finish. IF you like it, coat it with oil, or Wonderlube( my choice), and the part is ready to be installed.
You can do barrels the same way, although you are obviously working with a larger surface that is harder to keep hot. I move the propane torch from one section of the barrel to the next, and brown about 5-6 inches at one time. After the 3rd application, the finish seems to run together and you can't tell where one effort began and the next ended. I have been able to stop after a third application of browning when I have taken extreme pains to make sure I have covered all surfaces evenly. The last two coatings were not necessary. Why take several days or even weeks to brown something if you can be done with it in 2-3 days? Steel oxidizes really fast when it is hot, and acid is applied.