In a joomla article, you need to use the loadposition system to load your module :
docs.joomla.org/How_do_you_put_a_module_inside_an_article%3F
Then, create a menu item to that article so that you can copy the link and then put that menu on a hidden main menu.
Then, in the file I was talking about, you can add such code:
$app =& JFactory::getApplication();
$app->redirect('URL_OF_YOUR_MENU');
just after:
if(!$this->identified){
and voilà. If a user access the checkout without being logged in, he will be redirected to your article with the login/registration module in it.