Voicemail 100% full but keep getting messages

[iMas70]

It's rare that I get voicemail messages that mean something so I've been letting my VM fill up. I planned to keep it at 100% for awhile so I won't get any new messages. I even had my girlfriend call to leave a few 4 minute messages (music) to fill it up. I received a message that said my VM was full but I still get messages. The same thing has happened before I called AT&T about this a few times. No help there. They said Apple might be able to help me (visual voicemail).

Any suggestions?

 

[iMas70]

Put another call into AT&T but still no help. I've received 16 voicemails after I received a messaging saying it was 100% full (didn't delete anything).