Humans migrated to the Americas by at the latest 8900 BC when the land bridge disappeared, and we have evidence for migrations way before that. There's no way any kind of genetic change that occurred around 3000 BC could have made it to the Americas, and the indigenous population does not seem to exhibit such divergent modes of thought. They are essentially modern humans. So this date needs to be pushed way back.
No, Jaynes posits it happened as recently as 3000 BC, and bases the hypothesis on evidence from sources that are far more recent than 70 kya (not that we have any literary sources that are 70 kya old)