HaLeiVi, your theory is that Titus ym”s took the Yidden from Eretz Yisroel to Rome, and from there they spread to Ashkenaz (i.e. the German King Charlamagne.) Thus Ashkenaz shtams more from the Yidden in Eretz Yisroel than from Bavel. This is the opposite of what ItcheSrulik proposed.
Either way, there is no evidence indicating any more conclusively whether the Sefardim shtam more from E. Yisroel or Bavel, or whether the Ashkenazim shtam more from E. Yisroel or Bavel.