I have not tested form rules on multi-select fields but I�ve take your word for it that they don�t work for the has changed rule.
But if you make a new formula Text field
ToText([my multi select field])
Then you will have a text field and presumably the form role will work. But you will need to have this field be on the form it�s self so that the form will remember to recalculate it. You don�t need to have a visible on the form so you can create a dummy form rule to hide it but it does need to be on the form.