Seems like an interesting idea to me.
I think you're exaggerating when you say the Senshi have
a shoot first/ask questions later attitude. As I recall
whenever they encounter monsters, the monsters are
always attacking someone. In contrast when Luna mis-identified
the other Senshi as possible monsters the girls always 
investigated first.
So maybe you'll want your possessed characters driven to
attack and their friends have to both protect and restrain
them. Something similar was done in a very good Ranma/ADP
short crossover story-Akane had gotten a lot of cyber upgrades
that sent her over the edge when a red haired sales clerk asked
if she wanted a padded bra.

BTW does anyone remember the number or title of that short story
Anita Blake/ Devil Hunter Yohko/ Ranma crossover?