In my experience, although aggravating, the after-rust will settle down over time. It would be best to de-oil the barrel before boiling and brake cleaner would do a good job of that. Once de-oiled, you could soak it in a strong washing soda solution if you don't want to go from brown to black. Washing soda is a much stronger base than baking soda and, in my opinion, is a superior neutralizer.