DURING THE ANAPHORA!
More to the point, as Fr. Archimandrite Robert Taft, S.J. puts it: the miracle of the Eucharist is not to turn bread and wine into the Body and Blood of Christ but to turn you and me into the Body and Blood of Christ! Pope St. Leo the Great wrote, "In the Holy Eucharist man becomes What he consumes."
Thanks for your question, and your independent study of the Divine Liturgy and Eastern Catholicism is admirable.
It is interesting that you have stumbled on one significant area which highlights a noteworthy difference between Eastern and Western thought as expressed in the Divine Liturgy. The quotes above are certainly relevant to that understanding. I would only add that we consider the sacraments to be mysteries. As such, we cannot fully understand all aspects of these mysteries, which would make it difficult to identify the exact moment in which the bread and wine become the Body and Blood of Christ. As such, the "Words of Institution" do not hold the same emphasis as in Western thought, and we generally hold that the transformation occurs at some point during the entire Anaphora.
Although one always has to be somewhat cautious with this source, there is a decent Wikipedia article on this subject.
http://en.wikipedia.org/wiki/Words_of_InstitutionThe article makes one interesting point and observation:
No formula of Words of Institution in any liturgy is claimed to be an exact reproduction of words that Jesus used, presumably in the Aramaic language, at his Last Supper.
Further, the article correctly points out that some Eastern liturgical expressions do not use Words of Institution at all, further emphasizing the aspect of mystery ascribed to the Holy Sacraments / Mysteries in Eastern thought.
Bless you in your quest for greater understanding and appreciation!