it would require recomputing the Earth's history from the time the AGI is activated back to the death of the last person it intends to save.

Doing it this way sounds a lot harder than discovering the initial conditions of the universe and then simulating forward, checking the simulation against conditions at the time the AGI exists in. Then you just pull people out of the simulation when they 'die' on Earth.

The probability for this being possible follows the probability of the Simulation hypothesis. As for the ethics of it- I'm not convinced the existence of additional copies information theoretically indistinguishable from already existing people alters the relevant moral calculations one iota.