That was interesting, because -- as far as we know -- we don't have voicemail from AT&T.
I spent some time messing around and eventually managed to clear the message. Then I went online to check our account to see why it might think that we were supposed to be getting voicemail.
And I discovered that my long distance provider was still Sprint and that we still had call waiting.
So I called again. This time, the wait time of one minute was actually accurate and I got a nice woman who reported that there was no record of my previous call. Further, I should have been transferred to a third-party verifier for the change in long distance service, which -- surprise! -- hadn't happened on that previous call.
We have now changed the service again. And the helpful lady has credited me for the call waiting time during which the service was supposed to have been turned off.
I even spoke with the third-party verifier.
And back to work...