Moving Comments

The hook part isn't part of your original code:

add_shortcode( 'some_content', 'insert_before_comments' );
function insert_before_comments() {
    ob_start(); ?>
        <ul class="post-meta">
            <li>Distance: <?php echo get_post_meta($post->ID, 'Distance', true); ?></li> 
	    <li>Time: <?php echo get_post_meta($post->ID, 'Time', true); ?></li>  
	    <li style="font-weight:500;"><?php echo get_post_meta($post->ID, 'Download', true); ?></li>  
	</ul>  
    <?php
    return ob_get_clean();
}

Then your shortcode should be [some_content]. If this doesn't work then unfortunately we might be out of ideas.

Oh I see then I'd just need to add the shortcode [some_content] at the bottom of each post when creating it?

Yup or add them through the hook I suggested before.

Untested...

I've discovered I can just add my custom fields to the GP Hooks 'After Content' hook which works perfectly and then just hide/display sidebar as necessary with CSS.
However, going forward I will need the custom fields to only display on posts in certain categories. I've tried the following but it doesn't display and my sidebar and footer disappear:

<?php if ( in_category( 'mountainbiking' )) { 
    <div class="mobile-summary" style="margin-top:30px;">
		    <aside class="widget"> 
		      <h2 class="widget-title" style="font-size:22px;">Route Summary</h2>
		      	
			    <?php the_meta(); ?>
		    </aside>	
	</div>
}
?>

Try in_category( 'mountainbiking' ) && is_single()

Here's my full code now but it's still not working:

<?php if ( in_category( 'mountainbiking' ) && is_single() ) { 
    <div class="mobile-summary" style="margin-top:30px;">
		    <aside class="widget"> 
		      <h2 class="widget-title" style="font-size:22px;">Route Summary</h2>
		      	
			    <?php the_meta(); ?>
		    </aside>	
	</div>
}
?>

Just to clarify, if I remove the if statement and just leave the HTML and custom fields they display fine.

Try this instead:

<?php if ( in_category( 'mountainbiking' ) && is_single() ) {  ?>
    <div class="mobile-summary" style="margin-top:30px;">
		    <aside class="widget"> 
		      <h2 class="widget-title" style="font-size:22px;">Route Summary</h2>
		      	
			    <?php the_meta(); ?>
		    </aside>	
	</div>
<?php } ?>

Thank you Tom, works like a charm. Obviously didn't quite have my PHP syntax correct.

No problem, glad I could help :)