The Ashkenaz bottleneck was “between 600 and 800 years ago,” but the Ashekenaz - Sefardi split goes back a few hundred years before that, as evidenced by Rabbenu Gershom, whose prohibition of polygamy was binding on Ashkenazim but not Sefardim.
Most likely a larger Jewish population in Europe was all but wiped out at the bottleneck, possibly fallout from the Crusades.
...and don’t forget the Black Death. That wiped out a third to one-half of all Euros. If a significant percentage of Jews back then lived in more urban environments as they do now, they would have suffered more from plagues than the country folk.
Jews (Safardi) took a big hit prior to 1492 when Jews who would not convert were expelled from Spain, mostly to north Africa. Then there was the great plague which decimated Europe between 600 and 800 years ago. If Jews were condemned to ghettos and very poor villages they may have died in greater quantities than the Christians because of more rats and poorer nutrition. How did Jews feel about cats as pets?
More likely the plague, and the follow-on persecutions.