This is what finally worked for me.
To pull in the banner (featured) image from another page, create the search-results page in WordPress and make sure it is excluded from the search results by using the Search Exclude plugin, then add your featured image and pop this into your two-column custom template:
<?php if (is_search()) {
$attachment_id = 1711; // attachment ID
$image_attributes = wp_get_attachment_image_src( get_post_thumbnail_id($attachment_id), 'full' ); // returns an array
if( $image_attributes ) { ?>
<div class="top-background" style="background: url(<?php echo $image_attributes[0]; ?>) !important;"></div>
<?php }?>
<?php }?>
To force wordpress to make use of the two column custom template as your search results page:
<!-- SEARCH PAGE -->
<?php if (is_search()): ?>
<section class="entry-content clearfix" itemprop="articleBody">
<ul>
<li>
<h3><a href="https://wordpress.stackexchange.com/questions/144043/<?php echo get_permalink(); ?>"><?php the_title(); ?></a></h3>
<?php
$content = get_the_content();
$trimmed_content = wp_trim_words( $content, 40, '<a href="'. get_permalink() .'"> ...Read More</a>' );
echo $trimmed_content;
?>
</li>
</ul>
</section>
<?php endif ?>