The results you got using Evaporust are pretty much identical to what you'd see using a solution of molasses and water. The big differences are that the molasses solution typically takes longer, but it costs a fraction as much. I can fill a plastic 55 gallon drum of Molasses solution at a 5-6 parts water to 1 part molasses for around $20.00. It's very hard to find Evaporust for under $20.00 a gallon, even in bulk. I still use Evaporust, but only when removing rust from small items or gun parts indoors during the winter months. Both products work quite a bit slower when used in colder temps.
Both methods rely upon the chelation of common red rust (Iron oxide hydrate), or in your case, the black iron oxide (Ferro ferric oxide) that we use as rust bluing. The oxygen atom is stripped from the iron oxide molecule, and the iron is left behind, no longer bound to the base metal. You can use either Evaporust or Molasses solution over and over until it gradually becomes depleted. When totally spent, the depleted solution is not toxic, and can be dumped around trees or shrubs to give them a shot of iron. Some sources say that the item must be completely submerged, or you may get pitting at the water (or sludge) line, but I have not seen that happen yet.
A while back, I bought a pair of 4 ft. Pony Bar Clamps for a buck apiece at a Swap Meet. They were fairly heavily rusted, and the screws were frozen. I thought about putting some penetrating oil on the threads, but instead just soaked them in a roughly 2 ft. deep container of Molasses solution for a week. After that end was rust free, I flipped ends and soaked the other end for another week. There was no sign of pitting at the point where they were above the solution. It also got into the rusted threads and freed them up. I now use a length of capped PVC pipe for soaking longer items. Some internet sources say that Molasses solution, (or Evaporust) may cause pitting on machined surfaces, such as engine blocks, cylinder heads, or tools. But I have forgotten about items left in my bucket of molasses slop for months, and found no such damage when I rinsed and scrubbed them off. I believe that if there is pitting after using these solutions, it was there all along, hidden under heavy rust. Neither product is going to replace steel or iron that is already gone.
Obviously, you'll be refinishing the barrels. I think I'd try ultrasonic cleaning for all of the other case hardened parts, rather than doing any chemical or abrasive cleaning. The results some guys have gotten are amazing.