Not to be flippant, but wouldn't one of the members of these groups have a copy of the group in their email? Given gmail and whatnot store things virtually indefinitely, couldn't the contents be recovered that way?
Some of these groups are decades old. For them, you'd be hard pressed to find someone who was there for the whole history of the group and kept them all. Also, yahoo was often a headache, dropping emails to individuals - you'd have to go to the website to read them. And furthermore, there is a lot more than emails stored on the platform: files/images/links/calendars/databases ...
To add to all this, it's not an individual project. Most people done' have technical competence. They need someone to help. That's what the Archive Team has been trying to offer (if not for Verizon).
-EJ