So your wanting the intro to use the parent page?
The only way to get this working that I know of would be by using custom fields.
Open up /wp-content/themes/awake/single.php and on line 17 you should see this,
<?php webtreats_teaser_text($post->ID); ?>
Change it like this,
<?php if (get_post_meta($post->ID, 'custom_title', true)) { ?>
<div id="intro_blurb">
<div class="inner"><?php echo get_post_meta($post->ID, 'custom_title', true); ?><h1></h1>
<div id="blurb"><?php echo get_post_meta($post->ID, 'custom_blurb', true); ?></div></div>
</div>
<? } else { webtreats_teaser_text($post->ID); } ?>
And then in each post where you want to change the title / intro enter a new custom field with a name of "custom_title" and a value of whatever you want the title to be.
The same with the blurb, a name of "custom_blurb" and a value of whatever you want the blurb to be.