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.
Heavens, I don't know how one can prove a point by calling it "pagan". It might just be possible that the pagans were right about some things you know.
the Bible clearly states
The Bible clearly states that we must eat the body and drink the blood - see John 6 as I quoted above, as well as the Pauline epistle quoted by another used. How do you interpret that away to NOT require the Eucharist?
"Pagan" and "wrong" are not synonymous terms.
the Bible clearly states that Jesus' sacrifice was a punctiliar affair
In what sense? Hebrews says he has entered into the heavenly Holy of Holies, there to offer his own blood on our behalf, and that he will emerge from there at the end of time to claim us. That's a direct reference to the Yom Kippur liturgy, with Christ taking the place of the High Priest.
It also means that the sacrifice is eternal, because it is eternally present in heaven.
In fact, there are no "punctiliar affairs" in heaven, because God is outside of time. Time is a created thing. God created it. He rules it, not the other way around.
only needed to be "presented" once
The issue is making the sacrifice present to us, in our time. How was the sacrifice made present to me, 2000 years ago, when I didn't even exist yet?