Thanks for the quick response. I have used the painter's tape with success for painting, but still had the same problem with the stain & varnish on the door. While the tape itself comes off cleanly & easily, the stain & varnish just seem to find their way through or under the tape. Also, I think I made the mistake of leaving the tape on for the entire finishing process (pre-stain, stain 2 coats, and 3 coats of varnish - all told, this could be a few days).
Perhaps I would be better off removing the tape between steps?
I might try the Pam idea. If I learn anything, I will post my findings.