How can I prevent an organic group administrator from accessing edit page of a group? I want them to be able to post content only, not edit the group itself.  I'm using og_read_only so they can only post content to their own group as well.  This module has a problem though, you have to select which content types are read only each time you create a group, and if you add content types, you have to edit all of your groups again and check off the new content type as read only.

Is there a module that can prevent the group admin from accessing the group edit page?  Would that module also be able to prevent the admin from posting to a group that they are not a member of?

I will accept an answer if it only covers preventing the group admin from accessing the edit page.  I was just hoping the other issue might be covered by the same module since they both seem related to access control.
My suggestion would be to use rules to redirect users that aren't admins to another page, or use hook_menu_alter() to alter the access permissions to the page. Alternatively, you can use hook_page_alter() to check the active user's roles and redirect them if they aren't in the admin group.