I was thinking, it wouldn't be illogical (no pun intended) for Spock Prime to go to Starfleet and just start telling them everything he knows about his timeline. The universe has already been altered in such a fundamental way that there's no reason to try and avoid it. Also, that's the easiest way to get everyone to immediately trust him. Once the location of the Doomsday Machine, Botany Bay and Guardian of Forever are confirmed to be true, who's gonna doubt him? Nobody, that's who.