as someone who polishes brass blades for antique fans, i've learned a thing or two about polishing.
first take it to a benchtop buffer with some mass cleaner (or brasso) and buff the hell out of it, if you still see spots what you can then do is take VERY fine sandpaper, and sand it all out then take it back to the buffer. i myself need to get a buffer, i use a dremmel to make do, but its slow-go.