Vague thoughts:
1) Would a Judaism that develops in an Italy that's more Muslim-dominated (at least through the High Middle Ages, late enough to pick up Jewish refugees from crusaders' pogroms along the Rhine) be counted as Sephardic?
2) I'm not totally sure whether it's more important to weaken Ashkenazim in Germany or in Poland. How would a much less tolerant medieval Poland affect the development of Ashkenazic culture?
3) A late idea that's probably not sufficient, but at least interesting: large-scale cattle plagues along the Rhine in the 17th century that get blamed on Jewish cattle traders, leading to pogroms and expulsions of German Jews?
4) An even later idea that's even less likely to work - prevent the German Jewish enlightenment in the 18th century? Without people like Mendelssohn, would Ashkenazim be as powerful in defining Judaic culture?
5) Getting later still: some sort of collapse of the Ottoman Empire in the mid-19th century leading to large-scale immigration of Sephardic Jews, particularly to the Americas? Essentially, give Sephardim more freedom to develop under the more tolerant American political climates, and it might have a larger claim to the center of Jewish life.