Hi benjoman,
Yes it's not possible to add allowed tags from the backend, but if you're really need that, you can modify the file
../modules/mod_relateditems_xtd/helper.php , at lines 377 you will see this code
$introtext = strip_tags($introtext, '<a><em><strong>');
try to change that to :
$introtext = strip_tags($introtext, '<h1><h2><h3><a><em><strong>');