Give extra post-meta to RSS feeds

I’m trying to extend an RSS feed to output some post-meta from my website.

I have an ‘event_date’ meta-key and I need to order by this as opposed to the RSS standard publish date, which I know how to do if I could get that information.

I’m using the following code, which makes use of the WordPress action hooks available in the RSS feeds. However, when I use these hooks, the feeds report that there are no items found, while without these the items are found, but of course I cannot order them as I need.

Am I doing something wrong in the way that I am outputting to the RSS feed?

/**
 * Adds the 'event_date' meta value to a feed
 */
add_action('atom_entry', 'add_event_date_to_feed');
add_action('rdf_item', 'add_event_date_to_feed');
add_action('rss_item', 'add_event_date_to_feed');
add_action('rss2_item', 'add_event_date_to_feed');
function add_event_date_to_feed(){

    global $post;

    $event_date_raw = get_post_meta($post->ID, 'event_date', true);
    if($event_date_raw && $event_date_raw !== '') :
        $date_object = DateTime::createFromFormat('D, d M Y H:i:s +0000', $event_date_raw);
        $event_date = $date->format('U');
    else : 
        $event_date = '';
    endif;
    printf("tt".'<eventDate>%1$s</eventDate>'."n", $event_date);

}