It should be noted that the Roman Canon does not have an explicit pre-consecration Epiclesis (if it has one at all) – the Holy Spirit is not personally invoked to change the bread and wine into the Body and Blood of Jesus Christ. There is the Quam oblationem prayer right before the consecration, but that is addressed to God the Father (Quam oblationem tu, Deus, in omnibus, quaesumus, …] facere digneris: ut nobis Corpus et Sanguis fiat dilectissimi Filii tui, Domini nostri Iesu Christi.)
There is a post-consecration epicletic prayer (the so-called “epiclesis of communion”) in the Roman Canon, the Supplices te: Supplices te rogamus, omnipotens Deus …] ut quotquot ex hac altaris participatione sacrosanctum Filii tui Corpus et Sanguinem sumpserimus. This prayer is directed not so much towards the change of the bread and wine into the Body and Blood, but towards our fruitful reception of the sacrament.
The Eastern anaphoras (except for one or two very ancient examples) do not have a pre-consecration Epiclesis; the Epiclesis always follows the words of Institution. The modern Eucharistic Prayers of the Roman Rite are a novelty in that regard, having the consecration after the Epiclesis, because Western theology (since Augustine, if not earlier) argues that the words of Christ bring about the change in the Eucharist.
I should also add that, at least in the early 20th century, official Orthodox teaching on the anaphora was that the words of Institution were read in a strictly historical and absolutely non-consecratory sense.