Possible solution -- called the FAA again today, and a very helpful
person in Medical Certification Customer Service told me if I faxed the
certificate in my possession to them, with a note of explanation, she
would change the number on my record to match the certificate I have.
Still no contact from the AME's office.

By the way, I neglected to mention that the AME's office also changed a
digit in my social security number. The FAA fixed that for me once
they found my record.