This was eventually resolved in an email exchange. I’ll post up the results here for anyone else having this problem.
Please note, you’ll need to be able to add and edit the PHP template files of your theme or Child Theme to implement this.
Here are the steps that resolved the issue over email.
These steps are done using the default twentythirteen theme. If the files have been modified, the code may not look exactly the same. But I presume that most of this will be left in place.
1. In your theme folder, you’ll find a file called single.php. This is the file that renders a single post item. You’ll want to copy this file and rename the copy to single-fdm-menu-item.php. This will tell WordPress to load this file when displaying a single menu item instead of the regular single.php.
2. Open up the new single-fdm-menu-item.php file and find this line:
get_template_part( 'content', get_post_format() );
3. Change this line to the following:
get_template_part( 'content', 'fdm-menu-item' );
4. Now, in your theme folder, find a file called content.php. Copy this file file and name the copy content-fdm-menu-item.php. Now, when a single menu item post is displayed, it will call single-fdm-menu-item.php, which will in turn call content-fdm-menu-item.php.
5. Open up the new content-fdm-menu-item.php file and find these lines:
<?php if ( has_post_thumbnail() && ! post_password_required() ) : ?>
<div class="entry-thumbnail">
<?php the_post_thumbnail(); ?>
</div>
<?php endif; ?>
Remove that line to remove the featured image display at the top of a single menu item page.