Dear Matthew Chatfield,
Thank you for contacting Styled Themes support team.
Depending on the post format you can overwrite respective template on child theme. let’s suppose if you are using default template then you need to copy content.php template on child theme, there you will find this following code:
<?php if ( is_single() ) : ?>
<?php the_content(); ?>
<?php else : ?>
<?php the_excerpt(); ?>
<a class="more" href="<?php the_permalink(); ?>" title="<?php the_title(); ?>"><?php _e( 'Continue Reading', 'scripted-pro' ); ?></a>
<?php endif; ?>
There you can change your text.
Let us know if you got any problems on this.
Thanks