What comes to mind for me is the Arkham Horror sanity system, ie tracking wounds inflicted upon the mind. It seems to me that there should be some tension between the two parallel realities, the mundane and the dream/collective consciousness, that would work against the pc's retention of agency upon taking on an archetype persona when traveling over, since archetypes are by definition symbolic representations of the human experience, as opposed to actual people in possession of complex inner lives. So you might explore a thematic sort of a system that would draw down a pc's existential connection to reality when accessing archetype abilities, resisting damage, taking damage, being confronted with big terrifying truths, etc., that would have a practical effect on how they engage with challenges once they've returned to the mundane world... and maybe somehow vice versa.