There is one more product that I have used to good effect, and that is
Miracle Cloth. It is a bit greasy and messy when used turning black, but it produces a shiny finish on brass that resembles buffing. I cut it into strips and "rag" the surface wearing latex gloves.
This is the before and after on a Mark VI restoration where Miracle Cloth was used on areas of the body that were not safe to buff such as around toneholes and posts. Some areas that were deeply scratched and pitted required some careful sanding prior to polishing.