Thanks again, Niblick.
I had a little mishap today with a pipe in my regular rotation, one of the few others with a vulcanite stem. I had to wash it with soap and water, which raised a very slight bit of oxidation. Rather than fart around, I used the toothpaste I have sitting near my pipe rack. I tell you, it worked nicely enough. Turned the rag brown as it adequately removed the oxidation. Reapplied Halcyon II Wax for a shine and layer of protection, and done, it was. I'm still going to try magic eraser with the double comfort, though.
I found this tidbit at pipesmagazine, user Wilson:
"With a magic eraser you can remove oxidation (it is, if I remember correctly, roughly the equivalent of 1500 grit sandpaper or 4000 grit micromesh)..."