Does the EO Church accept the possibility that the transformation may occur at one time during the Byzantine Liturgy, and at another time during the Latin Liturgy?There is no magical transformation moment in either liturgy.
When the Eucharist is offered at the beginning of the liturgy it is bread and wine. When you receive it, the body and blood of Christ.
The whole action of the liturgy makes this so, not a mere word or tinkling of a bell.
While I agree that it is the whole action of the liturgy which "enables" the transformation of the Precious Gifts (I say "enables" because God can, of course, do any thing), I do not buy into the analysis that the Gifts are in a "gradual process of becoming" the Body and Blood of Christ during the Liturgy*. I think perhaps that analsyis is an over-reaction to the Roman notion of the Gifts being instantaneously transubstantiated at the utterance of the words of institution.
We do not engage in the exercise of attempting to determine what minimum elements are required for the mystery to be effected. While many of us insist upon the inclusion of the epiklesis even in Western liturgies, I do not believe we hold the epiklesis alone or words of institution + epiklesis to be the only necessary elements of the mystery.
As has been said above, while we have the words of St John Chrysostom to the effect that the words of institution are the necessary element of the mystery, the blessed saint retained the epiklesis in the liturgy which bears his name (notably, it follows the words of institution). This seems to indicate that the words of the epiklesis are no less necessary for the consumation of the mystery.
Is my understanding on the right track?
* I am not saying this is your analysis.