I finally got through it last night. You have to let yourself get possessed by all three sisters to complete the encounter. I'm not sure if it's necessary, but I also turned around and defeated them in combat afterward as well.
To be frank, this is the first time I felt frustrated, even angry, with the game. The amount of time you, the player, have to spend doing nothing but wait for some chance to interact is insane . And all without any idea if you're even doing the right thing. Nor is there any kind of payoff at the end when you finish. It's not a very well designed scene, in my opinion.