Hmm, after doing a wee bit of thinking, I got a few ideas regarding some stuff that may have some relation with this time's "perfect possession" incident :
Anyway, going by the series general soul-related lore : from what I can tell, the body is basically the container of the soul, while the soul is like the thing where all the memories, experiences, knowledge and all such things pertaining to defining the individual is located. But the soul seems to play one more role, one where it shapes the body according to what it is : say Futo and Miko for example : in order to become what they currently are, they transfered their souls into some other vessels : in doing so, the vessels inside of which they transferred their souls somehow became their bodies ; take Mokou too for example : while her fighting style involves her taking severe damage and even occasionaly completely destroying her body, she will not only "resurrect" in her exact, same appearance, but will also somehow still remember past stuff, even though her brain, which is usually supposed to be the thing in which memories are stored, gets fried every single time she self destructs. No question about her clothes, please.
So, regarding the way the perfect possession incident present itself, in light of the previous points I mentionned, imo it seems pretty plausible to say that the girls turning into other girls when performing the "perfect possession" thingy might quite possibly have very much to do with their soul switching (which was already fairly obvious tbh). But to begin with, it's not like moving the soul around is obvious though, else a massive amount of people who are interested in immortality would've already went the Futo & Miko route : there's no way regular people's souls (or at the very least people who are not familiar with the way to do so) can be normaly able to move their soul around possessing people.
Point is, I believe it is quite possible that the "perfect possession" part of the incident might actually have something to do with souls getting dislocated or something around these lines ; an incident where other people's souls can get dislocated.
By any means, when it comes to people who somehow end up outside their bodies for no clear and apparent reason, I believe the first urban legend that comes to mind ought to be the Out of Body Experience ones. If it's just the rampant spread of the ability to use perfect possession, I can kinda see it as a consequence of the Out of Body Experience being misused or something around these lines. There's no telling what the actual responsible for the mess's intentions and motivations may be, though :X