Many thanks for all the suggestions. I spoke with the plumber who did the original installation and he said he had used silicone sealant rather than plumber's putty. He also stated that 50% of the jobs done around here (southeastern NH) are done this way.
His suggestion was to apply force, try carefully prying from the top and keep at it until it released.
My response was "You put it in, you deserve the job of getting it out! He accepted.