I may be close to a solution…

When wrapping the incorrectly displaying locked pages with:

   <?php if (current_user_can('edit_nav_menu_permissions')) : ?>
            <?php hkb_get_template_part('hkb-content-article'); ?>
            <?php the_excerpt(); ?>

<?php else :?>
Denied.
<?php endif; ?>

The menu shows “Denied” if the user cannot edit nav menu permissions. Obviously we don’t want to deny on this, but we want to deny on whether or not that user’s role is denied within the post.

Am I on the right track? If so, what should I be using instead of “Edit nav menu permissions”?

Thank you!