How can I only show published and public pages in menu?

Ok, here is the (next) problem:

Our restaurant has seasonal menus, of course. Each of them is featured on a separate page. Of course, only the page containing the menu currently available is published. The others are drafts or private pages.

Now I would like to add them all to the menu – but the menu only should show the currently public page.

That is to not being forced to give half the staff access to administrate the menus while enabling them to pre-work and write the menus, whenever there is time for it…

As the pages that are public and not-public/not-published change over the course of the year, if-menu or Menu Item Visibility Control seem not to be the right choice…

Thanks for any idea!