If you are interested in trying it, Kwik Set provided me with refinishing instructions for brass door latch sets, and may be an option in this instance. Much of the apparent deterioration is actually in the surface clearcoat, not the metal. Polishing does little good if there is a coating between the brass and the polish.
The procedure worked okay on our home entry set, but was a bit tricky. Simply put, you remove the outer clearcoat with paint remover, polish the underlying brass well, then apply a new protective clearcoat. This won't, however, deal with any true pitting issues.
Joel