For ten centuries the Eastern Patriarchates were in complete communion with the Pope, and they continue to recognize his primacy of honor today. There is no room for Reformed heresies in the East either, regardless of their views on the papacy.
The discussion, however, is not about the adminitrative structure but the Church Fathers being Catholic, and in order to refute that you need to find a patristic teaching that is recognized either in the West or in the East, which would be contrary to Catholicism.
Note that most Church Fathers are also saints of the Catholic Church: St. Ignatius, St. Irenaeus, St. Justin, St. Cyprian, St. Cyril, St. Basil, St. Ambrose. Those that are not, such as Origen Tertullian or Athenagoras are not canonized in the East either. Good luck.
Wrong...there were schisms occurring as early as the second century (Victor, Stephen, and Damascus - later the Acacian [AD 482], one under Patriarch Photios I of Canstantinople [AD 866], and continued through the Great Schism of 1054. It is a myth that there has been harmony amongst the patriarchs of the Early Church.