How to modify the action attribute of the wp-login.php?action=register form?

You should be able to hook into the register_form_validation hook (which may be the same hook you’re already using. I’m just not sure where they do the validation) and add something like:

function my_register_validation() {
if(isset($_GET['ref'])){ 
   header('Location: http://www.example.com/wp-login?action=register&ref=$_GET[ref]');

}
add_filter(' my_register_validation', 'register_form');

I think that is the right idea the code above is untested but I think it gets you on the right track.

You said you were adding it to a secret form value so you might be able to use $_POST['secret_value'] instead.