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
)
)
);