There is a pretty rough(albeit minor) translation mistake on page 29.
Refering to this statement from Battler: "The two of them did not commit suicide, nor did they kill each other."
When Battler talks about Natsuhi and Jessica not being being able to kill each other, the japanese line uses "douji" (同時) which implies that rather than them not being able to kill each other, they just couldn't kill each other at the same time.
The wording here is incredibly important to any potential solution.