Who determines the possession? The girls?
Your guess is as good as mine on that. That's why I pinged some folks who I believe are charismatics to this.
As far as the Church is concerned, this would be way, way, way off base.
But within charismatic circles, I don't know what their parameters are (a/k/a I don't know if they would consider this to be off-base or not).
Maybe the possessed determine the possession?
The onset/post-menstruation thing can make young girls say and do some bat-crazy things. Salem, Mass. in 1697 comes to mind.