I currently still have the menu item set to public and all of the categories and events set to their appropriate access level. When I set the menu item to public it seemed to fix the issue, however all items created after doing that now have the same initial problem and return the "Sorry - This item may have been updated while you have been viewing the webpage. Please try again" error when trying to edit an event.
Going in a re-saving the menu item did not resolve this, nor did re-installing the missing events plug-in.
It partially worked. When I set the related menu item to public everything that was there worked. But when new items were added the problem came back, so now all events after switching the menu item to public are kicking back the error, but the ones prior are working fine.