topcat54:
Fair question. While I have read, and continue to read as much of the Eastern Catholic and Eastern Orthodox tradition as I can, I am by no means as knowledgable on it as I am on the Catholic or more specifically, the Latin-Western Tradition as expressed by the Latin Fathers, St. Hillary of Potiers, St.Ambrose of Milian, St. Jerome, St. Augustine, etc.
However, given that there are some 30 million Eastern Catholic who share in the same Liturgical Tradition as the Eastern Orthodox, the only difference is that those Eastern Rite Catholics are in full communion with the Bishop of Rome and recognize the Primacy of the Church of Rome, I have done some study on the Eastern Liturgies and in fact have attended a Maronite-Catholic Liturgy, which is part of the Liturgical tradition from the Church of Antioch.
The Liturgy of ST. John Chrysostom dates to the 5th century and is the primary Liturgy of the Greek and Byzatine Tradition which you will find in the Greek-Orthodox as well as the Byzatine Catholic Churches, such as the Ukranian Catholic Church [Eastern CHurch in communion with Rome].
The other main Liturgies are the Liturgy of St. Basil the Great, dating to the 4th century, and the Liturgy of St. James which dates to 1st century. These 2 Liturgies are celebrated in the Eastern Orthodox Church on special Feast days, from what I gather. Here is a link to the Orthodox Church in the States that has both the Liturgy of St. Basil the Great and John Chrystotem.
http://www.goarch.org/chapel/liturgical_texts
I found this link from orthodoxwiki regarding the Liturgy of St. Basil The Great
http://orthodoxwiki.org/Liturgy_of_St._Basil
A short link on the Liturgy of St. John Chrystotem
http://en.wikipedia.org/wiki/Divine_Liturgy_of_St._John_Chrysostom
Now just a question, why would you assume that the Orthodox Divine Liturgy is not connected to the Liturgies of the Great Fathers of the Eastern Church, i.e. Basil the Great, John Chrystotem? Where did it come from? and again, lets leave your issues with the Catholic Church and Rome aside, we are talking about a Liturgy that has its own roots in the ancient Churches of the Eastern Roman Empire and those Liturgies are in essence, the same as the classic Roman Rite and its various sub-forms such as the Ambrosian, Mozarabic, Bregan, Sarum, etc, etc.