I have yet another dumb question.
How could the “great leap” have occured in all those divergent groups, considering that they had already diverged?
The Great Leap occurred 65,000 years ago, but not all groups participated equally. According to the author, the "humanity" was there in all of them, and they were all capable of making the leap (this I doubt), even if their group didn't do much with that inherent ability. They all may have begun using spears, etc., around the same time, but it's fairly evident some merely copied their neighbors, not invented new tools.
Because I doubt it. We've had ancestors as smart as (or in the case of Democrats, smarter than) us for a really, really long time.