We didnt even know the existence of that sick grand daughter till ep7 right?!
But the Nanjo killer theory in regards to Krauss and Natsuhi would kinda work if they still had some shred of trust in him. He might have convince them it was all fake and that everyone was waiting in the gazebo to trick Eva or something. So they came out with him and got strangled.
Ultimately I dont think it was him though. As I envision the scenario, Eva would have bolted out the door and Battler would follow at safe distance without her noticing. Nanjo and Jessica would stay behind. Culprit comes out and shoots Nanjo, shortly after that shots Jessica as well. Battler would have heard the first shot and would start running back, since he is closer he arrives first. Eva follows and finds him inside the room with Jessica and Nanjo dead. Wolf and sheep puzzle, Eva shoots Battler thinking he's the culprit.