I think the line…
$post = $a_z_query->get_the_item_object();
…needs to in the While loop a little further down than line 54. I tried the same instructions but kept getting RETURNed with an empty/null value even querying inside the While loop. Eventually I edited the code below, starting at line 54, in a-z-listing.php in my child theme taking this…
<ul class="az-columns <?php echo esc_attr( $a_z_listing_column_class ); ?>">
<?php
while ( $a_z_query->have_items() ) :
$a_z_query->the_item();
?>
<li>
<a href="<?php $a_z_query->the_permalink(); ?>">
<?php $a_z_query->the_title(); ?>
</a>
</li>
<?php endwhile; ?>
</ul>
…and replacing it with this.
<ul class="az-columns <?php echo esc_attr( $a_z_listing_column_class ); ?>">
<?php
while ( $a_z_query->have_items() ) :
$a_z_query->the_item();
$thumb = get_the_post_thumbnail_url($a_z_query->get_the_item_id(), 'thumbnail');
?>
<li>
<a href="<?php $a_z_query->the_permalink(); ?>"><img class="a-z-thumb" src='<?php echo $thumb; ?>' /><?php $a_z_query->the_title(); ?></a>
</li>
<?php endwhile; ?>
</ul>