I've had some thoughts about why, within the HPMOR world, it makes sense for Voldemort to choose to occupy a dementor-kissed body. I don't know the details about how the magic works or the solution to the HPMOR!mind-body problem, but it seems like it would be easier to take over a vacated body than to try to share the space with the original soul. It seems like a cleaner process, with no ambiguity about who's in control within the body. Second, based on Voldemort's personality (assuming that's what we're seeing from Quirrell) I think he'd prefer to be alone rather than having a roommate as he does in canon. Third, removing the original Quirrell also removes the need to rely on him to keep the secret and not give himselves away out of stupidity, lack of self-control, poor acting skills, or outright betrayal. Finally, other people might be able to tell when a body contains two souls - if the Sorting Hat can do it, why not the Hogwarts security system?