I asked over at the support forums and found an answer! I just had to wrap them in an additional containing loop to the template. Full answer can be found here in case any future person searching the forums needs it:
<?php /* Template Name: Your Custom Template Name */ ?>
<?php while ( have_posts() ) : the_post(); ?>
<div>Your custom content, including any template tags you want to use like <?php the_post_thumbnail(); ?></div>
<?php endwhile; ?>
https://wordpress.org/support/topic/problem-inserting-custom-post-into-page-has_rows-doesnt-appear-to-work/#post-9540245
