"I am the living bread that came down from heaven; whoever eats this bread will live forever; and the bread that I will give is my flesh for the life of the world." The Jews quarreled among themselves, saying, "How can this man give us (his) flesh to eat?" Jesus said to them, "Amen, amen, I say to you, unless you eat the flesh of the Son of Man and drink his blood, you do not have life within you. Whoever eats my flesh and drinks my blood has eternal life, and I will raise him on the last day. For my flesh is true food, and my blood is true drink. Whoever eats my flesh and drinks my blood remains in me and I in him."
Also, we do not "re-sacrifice" Christ - His death did that for all eternity. The Mass re-presents (notice the dash) the same sacrifice, as it is one for eternity, and not constrained by the linear progession of time as we know it.
You realise that what you just espoused is a pagan idea, right? Mircea Eliade had quite a lot to say about the religious use of "sacred time" which exists outside of or "under" profane time, and which views religious rituals as being eternal in the sense that their repetition is really partaking of the original or unitary act in "sacred time". What you just described with respect to the Catholic mass would equally apply to the ancient Mesopotamian akitu festival of the new year, and the sacred renewal of fertility via the sacred prostitution between king and priestess.
Sorry, but the Bible clearly states that Jesus' sacrifice was a punctiliar affair - it happened once, and only needed to be "presented" once. This is why Paul (or whoever) in Hebrews tells us that Christ is presently acting as our High Priest (i.e. sacrifice is done, now He can act as intercessor WITH that blood of atonement), and repeatedly emphasises the one-time-only, once-for-all nature of Christ's work on the cross.
As such, there is neither need nor warrant for "reading in" a bunch of pagan syncretism about "the Eucharist" which is not ever actually specified in the biblical text.