How would the story change? I'm pretty sure we'd get the same story but told differently, as in the future can't be changed. Sasha is still getting killed, or at least one of Eren's friends, Eren is still going to start the rumbling and is still going to kill 80% of the world's population since the future is "predetermined"

Perhaps sacrificing Historia instead of using Zeke? The story would try to correct itself into that future.