Membership - Creating groups limited by Membership type?

Is there a way that I can add a list on the groups creation settings page that will allow the creator to limit the group to certain membership types only?

Right now you can select public, private, hidden & an admin can go into backend and limit group to certain type of membership, but doesn't look like a member who is allowed to create groups can go ahead and limit it themselves.

Any way to make this work?

While I'm at it how do you add the membership name to a members profile or members listing.