Is the issue that the menu is appearing for all users, even if they are not administrators? I would recommend using a layout for non-admin users that does not have the menu bar on the left at all. Remove that region from the layout and use it for the non-admin home page. I would then make a separate admin user home page that takes advantage of a layout with that side bar region. Send the admin users here using the project navigation menu. If the admin and regular users see the same page when they log in (The grid with the 'inbox') then use a snippit to ensure the conten is the same on both pages.
Hope this helps,