Seeing that a lot of people seems to have missed it, I think it's best of me to comment here. Parka actually did a short chapter that shed some light regarding Zuikaku and her mental state, of which he/she uploaded to NicoNico (here's part 1, part 2 and part 3)
Unfortunately, account is required to view them so here's my interpretation of the chapter for those who are too lazy to sign in/didn't have account for NicoNico (spoiler obviously):
J( ´.`) 'confronts' her not-so-sane alter ego in an ephemeral plane, where it is revealed J( ´.`) is actually a defense mechanism from keeping Zuikaku's sanity from crumbling under the guilt of Takao's demise, it is also implied that Zuikaku sank Takao in self-defense when Takao attempts to sink Zuikaku for some reason
