My favorite part is being able to rewind a few seconds. For example, people love to leave me a 3 minute voicemail and say their number at the end. If they say it too quick, I would have to go back and listen to the entire thing again.
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Forget the usual wimp "visual voicemail".
You sound like a prime candidate for those third party mailbox services where they not only give you the audio messages in any order, but also do a speech-to-text conversion and send that to you. I hear it's great for people who're constantly having to write down directions and numbers.
Not to mention that you'd be able to "read" your voicemail and not disturb the meeting.
Google around. Most companies have try-out periods.
http://www.callwave.com/landing/corp_home_v2e.asp