That description sounds great. I had originally proposed a mockup for the group page but am not wed to that design specifically.
A PM seems fine, but recall that new users can’t send PMs immediately so it could limit the use case of asking new users to “please sign up for our group.” I used groups for an event and had to move the PM setting down to TL0. No need to start the “PM settings” debate again, (although I would be in favor of letting TL0 users PM admins as a setting). Seems like TL0 users would need to be able to PM group owners for this feature. If an admin or moderator is going to ask for invites, they should be willing to manage the PMs.
From a design standpoint, it would be nice to remove the left rail (or manage via CSS) since those items seem to cover posts based on users not the group?
Adding a groups page would be ideal if you can fit it in to 1.7 Thanks very much.