FYI.
For anyone that wants to add custom fields to this page (maybe a better way, but this works for my purposes):
With the above code included anywhere below this:
/**
* Profile Information
*
* ...
*/
In shortcode-profile.php, scroll down to where the fields get updated (around line 290, just before the “wp_update_user” call):
update_user_meta( $user->ID, 'meta_name', 'meta_value' );
This adds the custom meta field to your user’s profile.