the vast majority of people who have ever existed lived during the period of modern recorded history

You sure about that, this says that 117 billion people of our species have ever lived. Writing is around 5,000 years old, and initially was used for accounting so history doesn't come around until later, whereas the species is 200,000 years old.

Idk what your classifying as the period of modern recorded history though. Maybe you could say that period started in the 2nd or 3rd millennium BC in the middle east, but that doesn't mean it started everywhere. At that time there were tons of people who lived without writing, and that continues on until very recently. So even after history was "invented" only a fraction of people lived under societies that practiced it until ~200 years ago.

I'm not going to do all the math but it seems to me a majority of people who ever lived, were not a part of societies that recorded history.