I would like to weigh in and say that I think a Google group would be an awesome way for the greeters to communicate. In addition to clearing the "clutter" from our feeds, it would also be a lot easier to follow along with the threads of our conversations and catch up on what happens when you're away.
And because of how it's structured, there would be an ongoing "archive" that we could reference when we have a question about something.
If you're not familiar with Google groups, it's structured like a forum -- similar to G2G -- but we would have the capability to keep it amongst only the greeters, so if there was a sensitive topic we needed to discuss, it could be done in private.
Just my opinion. :-)
ETA: I also meant to mention that there are a variety of ways to set up a Google group -- there's an email list, like Chris mentioned, but you can also set it up as a forum format or a Q&A format -- both of those allow email updates in addition to a web interface. There's also something called a "collaborative inbox," but I'm not familiar with how that works.