Is transubstantiation a Monophysite doctrine?

CrimsonCatholic and Perry Robinson participated a few months ago in a fairly technical but somewhat interesting discussion at David Waltz's blog.
CrimsonCatholic made a very interesting statement:

The key feature of Chalcedonian theology is that Christ's nature is exactly the same as ours, so what happens to the human nature in Christ happens to everyone who is "in Christ Jesus" (to use St. Paul's term) by grace, including the sharing of the divine glory.

I'd like to ask a few questions, if we're going to take this consistently with the rest of our theology.
So Christ's nature is exactly the same as mine. My nature is human. Part of being human (as opposed to being divine) is to be limited to a particular physical location at any one time, is it not? My body cannot be in more than one place at any one time. That's obvious.

Now, Christ Himself, at the time of His Incarnation, took upon Himself a human nature and a physical body. At the time of His Resurrection, His body became glorified and immortal; He doesn't necessarily have blood anymore, but He retains flesh and physical tangibility, among other properties. He can perhaps walk through walls, or perhaps not; John 20 simply says, "when the doors were shut where the disciples were, for fear of the Jews, Jesus came and stood in their midst and said to them, 'Peace be with you.'" Maybe He created a key and let Himself in; maybe He knocked and they let Him in; maybe He passed through the door via "teleportation"; the text does not tell us. Obviously He can perform miracles such as walking on water and perhaps passing through walls, disappearing right in front of two disciples at dinnertime on the road to Emmaus, etc, but we never see Christ in more than one place at any one time.

CCC 1376 The Council of Trent summarizes the Catholic faith by declaring: "Because Christ our Redeemer said that it was truly his body that he was offering under the species of bread, it has always been the conviction of the Church of God, and this holy Council now declares again, that by the consecration of the bread and wine there takes place a change of the whole substance of the bread into the substance of the body of Christ our Lord and of the whole substance of the wine into the substance of his blood. This change the holy Catholic Church has fittingly and properly called transubstantiation."

1377 The Eucharistic presence of Christ begins at the moment of the consecration and endures as long as the Eucharistic species subsist. Christ is present whole and entire in each of the species and whole and entire in each of their parts, in such a way that the breaking of the bread does not divide Christ.

1378 Worship of the Eucharist. In the liturgy of the Mass we express our faith in the real presence of Christ under the species of bread and wine by, among other ways, genuflecting or bowing deeply as a sign of adoration of the Lord. "The Catholic Church has always offered and still offers to the sacrament of the Eucharist the cult of adoration, not only during Mass, but also outside of it, reserving the consecrated hosts with the utmost care, exposing them to the solemn veneration of the faithful, and carrying them in procession."

1379 The tabernacle was first intended for the reservation of the Eucharist in a worthy place so that it could be brought to the sick and those absent outside of Mass. As faith in the real presence of Christ in his Eucharist deepened, the Church became conscious of the meaning of silent adoration of the Lord present under the Eucharistic species. It is for this reason that the tabernacle should be located in an especially worthy place in the church and should be constructed in such a way that it emphasizes and manifests the truth of the real presence of Christ in the Blessed Sacrament.

1412 The essential signs of the Eucharistic sacrament are wheat bread and grape wine, on which the blessing of the Holy Spirit is invoked and the priest pronounces the words of consecration spoken by Jesus during the Last Supper: "This is my body which will be given up for you. . . . This is the cup of my blood. . . ."

1413 By the consecration the transubstantiation of the bread and wine into the Body and Blood of Christ is brought about. Under the consecrated species of bread and wine Christ himself, living and glorious, is present in a true, real, and substantial manner: his Body and his Blood, with his soul and his divinity (cf. Council of Trent: DS 1640; 1651).

On any given Sunday, or really most any day of the week, Mass is performed at thousands of churches across the globe. On any given Sunday morning, to be sure, the Eucharistic host is transubstantiated in multiple locations, at the same time. How well does this match with the conception of Christ's body's substance? It is supposed to be of human substance, yet here it displays a trait better assigned to divinity, that of omnipresence. Christ's human body, it turns out, is NOT "exactly the same as ours", as I don't think CrimsonCatholic has ever been at two or more places at once. I know I haven't, much as I'd like to be; I could get a lot more accomplished!

And the situation seems to be even worse than that. Take a look at this from the Catholic Encyclopedia:

On the contrary, He continues His Eucharistic Presence even in the consecrated Hosts and particles that remain on the or in the ciborium after the distribution of Holy Communion.

Thus the red candle/light that one often sees perpetually lit on the altar of a Roman church - one or more transubstantiated hosts are still there. The real and substantial body of Jesus Christ is enclosed there. In many hundreds or thousands of churches across the world, simultaneously.

So, taking the doctrine that CrimsonCatholic has expressed and applying it consistently across the board, we run into a serious snag in the doctrine of the Eucharist. It would seem that, if transubstantiation is true, then the RC position leads to a denial of the true human nature of Christ, because the substantial, real human body of Christ is simultaneously in thousands of different places, thus applying a divine trait to Christ's human nature. Not Chalcedonian at all, then; more like Monophysite.