The manual has a still-working 800 number in it, right there in the paragraph about what to do if you lose the admin voicemail password. Just the Avaya support line, it seems. Awesome it still works after 20 years.
Unfortunately, they were unable to help me. I have all the original purchase paperwork from when it was installed in 2000, and offered to open up a new support contract or pay a one-time fee, but they said that they no longer make new support contracts with end-users who have old systems.
I am experienced with equipment like this. I did try connecting to the serial console, but couldn't get any response. Might be a baud rate issue. The documentation I found said 19200, but I never got a response.
I also found a document suggesting I log into mailbox 9997 with the device serial number as my password. That also didn't work.
It seems like there's a piece of carefully-guarded knowledge that would make this a ten-minute job if I had it, and so I am pursuing that knowledge.
-- David