Thanks to all for all of the varied suggestions (which I will definitely
keep in mind for future projects). WD-40 did the trick here; letting
the tape soak for 2-3 hours loosened things up enough so that the "tape"
portion came right off, leaving behind the dried adhesive. Soaking that
for another couple of hours softened it to the point where it scraped
off easily with just a fingernail.
This also worked on the three panel switches that had masking tape
applied, however the adhesive appears to have marred the surface of
these switches a bit (not so much that it's really that noticeable, though.)
Now that it's all cleaned up, it looks very very nice. I'll take some
pictures tomorrow.
- Josh