For the rim, I just used some 180 grit sand paper, laid it on the table and sanded away. I bet I went down nearly 1/8 inch (I compared it to another new Peterson tankard that I own, and this one is definitely shorter now). Then I used some 600 grit paper to round out the bowl from the inside.
I also removed the silver thingy and sanded all around the outside of the pipe with various grits (there's a rundown earlier in the thread, I followed that recommendation). Once it was baby's butt smooth, I added the two coats of the minwax, waiting overnight between coats and hitting it lightly with 0000 steel wool in between.
I glued the silver piece back on using some epoxy that a local woodworking store told me would stand the heat and not produce fumes.
Then two coats of carnuba and several coats of the aforementioned "pipe wax".
I couldn't be more proud of myself, as this pipe turned out much better than I expected...
Oh, and I paid something like $26 for the pipe on the bay, no lie!