I know how to do it on Sprint/Nextel, I'd say its worth a try on your verizon.
On sprint/Nextel call your cell from a landline, (ofcourse the landline has to have a conversation recording, most w/ voice messages do), let it ring, then you will hear you greeting..as soon as you start hearing your greeting..press the * button, then it stops your greeting and operator says "please enter your password" (voicemail password ofcourse). After this, just record your conversation. hope it works on your verizon.

Hi, first time poster here. I did some searches on "voicemail" and "voice mail" and didn't see this addressed anywhere, so I apologize if this has been asked before.

I have one spot left on my voice mails, and I'm trying to find a way to save my existing voice mails to free up more, if not all, of my slots. Anything new I want to save can't be at this point, so I was hoping there was a way to forward my voice mails somewhere else to be saved in any kind of format (to exclude another mobile account). Ideally and ultimately in .mp3 format.

Any help or nudges in the right direction would be greatly appreciated.

Not sure if it's relevant, but just in case, my provider is VZW.

TIA,
Shane