Except that Harry didn't have access to his time turner prior to witnessing Hermione's death. Once something has happened it cannot be re-written in the self consistent time travel of the HPMORverse.

Harry did ask Dumbledore about ways to create the illusion of death in order to get around this hurdle (essentially allowing the information to be the appearance of Hermione's death as opposed to her actual death), but the Headmaster said he had tried something like that with disastrous results previously.

I know of nothing in the known rules of time travel in HPMOR that wouldn't allow for Harry to plan to swap gems. In fact, he used basically this exact same trick for the Remembrall and Torture incidents.