I've tried Brasso, Flitz and a couple of other cleaners that don't really get the job done.
You're sure it's not laquered? I haven't seen many authentic brass spittoons that weren't. (Dad used to collect stuff like that) They were usually laquered because spit, tobacco drippins and whatnot are hard on metals. In fact, most every brass anything is coated with laquer to keep it from oxidizing. If it wasn't laquered, you should have noticed quite a bit of tarnish on it. Check out the bottom of it. Was it shiny to begin with? If it was, you might have a problem after using brasso. If you took the laquer off, it will turn a brownish color PDQ. Usually it occurs in spots.
As for the stains... You *might* try ammonia. I know it works on bare metal. Maybe somebody who knows more about laquers will come along and give some advice on that. You might also try a mild soap and some hot water. It shouldn't damage anything. If you have stripped the laquer, you'll need to remove the rest of it to keep it from looking shabby. Some steel wool or extremely fine sandpaper should do the trick. Once the rest of the laquer is removed, polish it up with brasso, and then give it a coat of olive oil to prevent oxidation.