God, wouldn't you know it?
As soon as I posted this, the mysql.mydomain.com page went to a dialogue where I was asked for a user name and password, which (for some reason) failed. I went back, deleted the user (because I suspected that the password having a special character in it might have caused the failure. I am now giving that a minute to work its way through the system.
mt-load.cgi is stil returning a "mysql.mydomain.com does not exist" error, though fixing the password may solve that. We'll see.