Add to this what Aquinas says in De Ente et Essentia -namely that in God, essence and being are the same, The kind of "Thing" God is is an "Existing Thing". Yet, I am hearing now that God's essence is Relation. I am thinking this is one of those Catholic both/and things (God's essence is somehow both Existence and Relation) but am as of yet not understanding how so.
The Church doesn't teach philosophy, not even that of Aristotle and Aquinas! Revelation is the Person of Jesus Christ Who is the Word of the Father. Faith is the response of the whole person of the believer to the act of self-gift that the Father makes in the Person of the Son.
"Substance" is a conceptual sign that Aristotle created to formulate a likeness between his experience of being through sensation of particularly organic reality like animals that grow, heal, etc., and the inorganic that perdures in spite of what he perceives to be "accidental" like bigger/smaller, white/black, etc. "Substance" pertains to the experience of internal and external sensation of being and the mode of our abstract knowing through concepts. I would even dare to say that "substance" corresponds to our conceptual way of knowing.
"Substance" as conceptualized by Aristotle is designed to account for and represent "being-in-itself." "Accident" is designed to account for "being-in-another." Neither of these categories could account for reality that is pure self-giving or streaming out of self as revealed concerning the Trinity. Hence, none of the divine Persons could be classified as "substances." And hence again, God could not be called a "substance" because there can be no "accidents" in what we know of God, since "He" is not susceptible of change having nothing that is not totally "Himself."
In a word, "substance" is a useful category to give being, and has been its prime category. But reality has proven larger than "substance." "Communio" that is Magisterial designation of the Trinity transcends substance since it is understood to be integrated by persons whose very "to be" is "to - be - in - relation." This is beyond our sensation, but it is not beyond our experience. You experience this in spousal love (and for that I direct you to JPII's "Love and Responsibility" Ignatius 96).
To shorten this, I include Ratzinger's remarks on the category on "substance." (I also direct you to Wojtyla's "Subjectivity and the Irreducible in the Human Person" in Person and Community Lang (1993) 209-215).
Re: the "essence/esse" duality, you are here in the epistemological horizon of the experience through the senses. Neither Aristotle or Aquinas knew anything of "experience" of the "I" in the moral moment (such as faith as anthropological act. Aquinas understood it in terms of viritue/habit/accident of substance). Vatican II, JPII and Benedict are always dealing with faith as an anthropological act of the entire "I" that is given to the revealing "I" of the Logos. When you talk about the "essence" of God, you are making an abstraction. The existential revelation is "I AM," and Jesus Christ reiterates that He is "I AM" in Jn. 8, 24, 28, 58. See the Greek does not say "I am he," but ego eimi.
With regard to the Eucharist, Ratzinger is at pains to explain that the "body" of Christ is not a substantial -in-itselfness. No human body is, much less Christ's, particularly when dealing with the risen body of Christ, which is what we consume.
"The body is not just 'there,' having a merely external relationship to the spirit; rather, the body is the self-expression and 'image' of the spirit. In the human being, what constitutues biological life also constitutes the person. The person actualizes itself in the body and the body is, therefore, its expression. In the body we may see what is invisible as spirit. Because the body is the person become visible, and the person is an image of God, the body, taken in its full network of relationships, is also the space where the divine becomes imaged, expressed, seen" J. Ratzinger, "The Paschal Mystery as Core and Foundation of Devotion to the Sacred Heart," in Towards the Civilization of Love" Ignatius (1985) 149.
“Substance” in Joseph Ratzinger
1) “In this idea of relativity in word and love [that is the person in God], independent of the concept of substance and not to be classified among the ‘accidents,’ Christian thought discovered the kernel of the concept of person, which describes something other and infinitely more than the mere idea of the ‘individual.’ Let us listen once again to St. Augustine: ‘In God there are no accidents, only substance and relation.’ Therein lies concealed a revolution in man’s view of the world: the undivided sway of thinking in terms of substance is ended; relation is discovered as an equally valid primordial mode of reality. It becomes possible to surmount what we call today ‘objectifying thought;’ a new plane of being comes into view”1 (Josef Ratzinger, “Introduction to Christianity,” Ignatius  132).
2) More recently, he refers to “person” as a “new philosophical category… a concept that has become for us the fundamental concept of the analogy between God and man, the very center of philosophical thought;”2 J. Ratzinger, “The New Covenant,” in Many Religions – One Covenant Ignatius (1999) 76-770).
In the light of this, he remarks:
“The meaning of an already existing category, that of ‘relation,’ was fundamentally changed. In the Aristotelian table of categories, relation belongs to the group of accidents that point to substance and are dependent on it; in God, therefore, there are no accidents. Through the Christian doctrine of the Trinity, relatio moves out of the substance-accident framework. Now God himself is described as a Trinitarian set of relations, as relatio subsistens. When we say that man is the image of God, it means that he is a being designed for relationship; it means that, in and through all his relationships, he seeks that relation which is the ground of his existence”3(Ibid) 3)
“I believe that if one follows this struggle in which human reality had to be brought in, as it were, and affirmed for Jesus, one sees what tremendous effort and intellectual transformation lay behind the working out of this concept of person, which was quite foreign in its inner disposition to the Greek and the Latin mind. It is not conceived in substantialist, but… in existential terms… Remaining on the level of the Greek mind, Boethius defined ‘person’ as naturae rationalis individual substantia, as the individual substance of a rational nature. One sees that the concept of person stands entirely on the level of substance. This cannot clarify anything about the Trinity or about Christology; it is an affirmation that remains on the level of the Greek mind which thinks in substantialist terms.” (J. Ratzinger, “Concerning the Notion of Person in Theology,” Communio 17 [Fall, 1990] 448).
Let me suggest more. If the bread becomes the Body of Christ, and the Body of Christ is His Person, and His Person is an action of self-gift (relation) to the Father, then the Body of Christ is an Action, a divine Act ion. Cartesian dualism would have the body to a substance in itself as “res extensa.”
Let me add re: the Body of Christ is His Person.
From the time of the Council of Chalcedon (451) to Constantinople III, the problem was a kind of “parallelism” of the divine and the human, with the “human” as a kind of “thing-in-itself” as “substance.” Ratzinger had this to say: “In the manuals, the theological development after Chalcedon has ordinarily come to be little considered. The impression thus frequently remains that dogmatic Christology finishes up with a certain parallelism between the two natures of Christ. This impression has also been the cause leading to the divisions since Chalcedon. But in effect the declaration of the true humanity and the true divinity of Christ can retain its significance only when there is a clarification also of the mode of unity of the two natures, which the Council of Chalcedon has defined by the formula of the `one person’ of Christ, at that time not yet fully examined. In fact only that unity of divinity and humanity which in Christ is not parallelism, where one stands alongside the other, but real compenetration, - compenetration between God and man – means salvation for humankind. Only thus in fact does that true `being with God’ take place, without which liberation and freedom do not exist…
“If God joins himself to his creature –man/woman – he does not wound or diminish it: he brings it to its plenitude. But on the other hand (and this is no less important) there remains no trace of that dualism or parallelism of the two natures, which in the course of history was frequently judged necessary to defend the human liberty of Jesus. Such studies forgot that the assumption of the human will into the divine will does not destroy freedom, but on the contrary generates true liberty. The Council of Constantinople has analyzed concretely the problem of the two natures and one person in Christ in view of the problem of the two natures and one person in Christ in view of the problem of the will of Jesus. We are reminded firmly that there exists a specific will of the man Jesus that is not absorbed into the divine will. But this human will follows the divine will and thus becomes a single will with it, not, however, in a forced way but by way of freedom. The metaphysical duplicity of a human will and a divine will is not eliminated, but in the personal sphere, the area of freedom there is accomplished a fusion of the two, so that this becomes not one single natural will but one personal will. This free union – a mode of union created by love – is a union higher and more intimate than a purely natural union. It corresponds to the highest union which can exist, the union of the Trinity…. (I)n Jesus there are not two `I,’ but only one. The Logos speaks of the will and human thought of Jesus using the `I;’ this has become his `I,’ has been assumed into his `I,’ because the human will has become fully one with the will of the Logos, and with it has become pure assent to the will of the Father.”
The Body of Christ is compenetrated with the divinity of the divine Person without losing its autonomy as natural freedom which is perfected as self-gift. The Body is the Body with its natural soul and human intellect and human will exercised by divine Son. St. Thomas said that there was only one Esse for the Body and Soul with its faculties of intellect and will, which was the Esse Personale (S. Th. III, 17 a.2, ad 2). Hence, that Body will be the material action of self-gift as Eucharist and to death on the Cross.
Now, let me add more from Ratzinger’s “God is Near Us:” “What does it mean, to receive the Lord? That is never just a physical bodily act, as when I eat a slice of bread. So it can therefore never be something that happens just in a moment. To receive Christ means: to move toward him, to adore him. For that reason, the reception can stretch out beyond the time of the Eucharistic celebration; indeed, it has to do so. The more the Church grew into the Eucharistic mystery, the more she understood that she could not consummate the celebration of Communion within the limited time available in the Mass. When, thus, the eternal light was lit in the Church, and the tabernacle installed beside the altar, then it was as if the bud of the mystery had opened, and the Church had welcomed the fullness of the Eucharistic mystery. The Lord is always there. The church is not just a space in which something sometimes happens early in the morning, while for the rest of the day it stands empty, ‘unused.’ There is always the ‘Church’ in the church building, because the Lord is always giving himself, because the Eucharistic mystery remains present, and because we, in approaching it, are always included in the worship of the whole believing, praying, and loving Church.
“We all know what a difference there is between a church that is always prayed in and one that has become a museum. There is a great danger today of our churches becoming museums and suffering the fate of museums: if they are not locked, they are looted. They are no longer alive. The measure of life in the Church, the measure of her inner openness, will be seen in that she will be able to keep her doors open, because she is a praying Church. I ask you all therefore from the heart, let us make a new start at this. Let us again recollect that the Church is always alive, that within her evermore t he Lord comes to meet us. The Eucharist, and its fellowship, will be all the more complete, the more we prepare ourselves for him in silent prayer before the Eucharistic presence of the Lord, the more we truly receive Communion. Adoration such as that is always more than just talking with God in a general way. But against that could then rightly be voiced the objection that is always to be heard: I can just as well pray in the forest, in the freedom of nature. Certainly, anyone can. But if it were only a matter of that, then the initiative in prayer would lie entirely with us; then God would be a mental hypothesis – whether he answers, whether he can answer or wants to, would remain open. The Eucharist means, God has answered: The Eucharist is God as an answer, as an answering presence. Now the initiative no longer lies with us, in the God-man relationship, but with him, and it now becomes really serious. That is why, in the sphere of Eucharistic adoration, prayer attains a new level; now it is two-way, and so now it really is a serious business.”
1 Josef Ratzinger, “Introduction to Christianity,” Ignatius (1990) 132.
2 J. Ratzinger, “The New Covenant,” in Many Religions – One Covenant Ignatius (1999) 76-770).
4 J. Ratzinger, “Concerning the Notion of Person in Theology,” Communio 17 (Fall, 1990) 448.
 J. Ratzinger, “Journey Towards Easter,” Crossroad (198 )
 J. Ratzinger, “The Presence of the Lord in the Sacrament,” God is Near Us Ignatius (2003) 89-90.