Use meta_query to get title of associated post

Try setting $title_search = get_the_title($post_object); and then using it in your query as 'value' => $title_search:

$args = array(
    'post_type' => 'journal_entry',
    'meta_query' => array(
        array(
            'key' => 'custom_author',
            'compare' => 'LIKE',
            'value' => $title_search
        )
    )
 );