In the past i have successfully browned barrels using just a salt water solution as suggested.
It must all be the same stuff but fine table salt was not great alone; sea salt was some what better but grit salt from an obliging grit box was the best, you could see the different metals rusting before your eyes on a hot humid day. Initially the solution was 1 tea spoon (heaped) to 1 pint cold water. Once the pattern was established with the solution further rusting was encouraged by dipping the barrels in cold water then leaving to rust in a humid environment
before
during
Finished article.