After disabling the options under ‘Logging’ and patiently waiting over night, everything seems to be in working order again. Suddenly I was able to view my log files again, and using the option ‘Delete Logs’, I deleted every log without any problem. It’s a mystery to me, but am glad to see that everything worked out just fine.
I used this as a solution for hiding draft pages. You can hide the (draft page) menu items with the li.draft class.
add_filter('nav_menu_css_class' , 'nav_menu_add_post_status_class' , 10 , 2);
function nav_menu_add_post_status_class($classes, $item){
$post_status = get_post_status($item->object_id);
$classes[] = $post_status;
return $classes;
}