Is that the halachah? I would think yes.
Neither Rashi nor Rabeinu Tam demanded that one wear the other’s tefillin. I would be hard pressed to say that one of them was not yotzei the mitzvah. If this is correct, then the order is not me’akev and even a random order is kosher. Maybe even l’chatchilah. The order would then be “kach nohagim” and nothing more.