Hello , I wanted to help with this rusty barrel thing. I actually cleaned up a 1873 model ,vand this is how I did it
Use a electro rust removal first. Non abrasive , and works only on rust , and does not remove any metal. Then to clean after get some fine steel wool and push it through the barrel with a spinning type cleaning rod.
Simply push a small wad of the steel wool just like a cleaning wad. Roll it into a tapered shape with fingers, and work it through the barrel over , and over until the desired shine is reached.
For the outside clean with steel wool , and then clean very well , and dry then use Van's gun blue. It does not smell , and works great. Oil the blue with 3 in one , or Remington oil.
I fixed this model 1873 barrel this way , and it came out beautiful, and shot great.