“If the body of Christ is really present in the Eucharist then it is the sacrifice of Golgotha that is happening, and St. Paul plainly teaches that it is present.”
Really? Where does Paul suggest Jesus is still being offered as a sacrifice at Calvary?
Yes, the Apostles and early church participated in the Eucharist...and gave it the name, ‘Thanksgiving’, not ‘Atonement’. Do this in remembrance of me...
Where he condemns those who do not discern His body, 1 Cor. 11:29. Also see 1 Cor. 10:16, the entire discourse there is about different understanding of the altar sacrifice:
16 The chalice of benediction, which we bless, is it not the communion of the blood of Christ? And the bread, which we break, is it not the partaking of the body of the Lord? 17 For we, being many, are one bread, one body, all that partake of one bread. 18 Behold Israel according to the flesh: are not they, that eat of the sacrifices, partakers of the altar? 19 What then? Do I say, that what is offered in sacrifice to idols, is any thing? Or, that the idol is any thing? 20 But the things which the heathens sacrifice, they sacrifice to devils, and not to God.
Note that he doesn't say "Israel eats of the sacrifices and we don't"; he compares the two sacrifices and says that one precludes another.
That the Eucharist is an act of thanksgiving is Catholic teaching: we come to thank Christ for His sacrifice. If no sacrifice were occurring at Mass, we could just as well do the thanking at home.
You may wish to head over to http://www.ccel.org/ccel/schaff/anf01.v.vii.vii.html where St. Ignatius ca. 100 says things like:
"Chapter VII.—Let us stand aloof from such heretics. They abstain from the Eucharist and from prayer,10161016 Theodoret, in quoting this passage, reads προσφοράς, “offering.” because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness, raised up again.
The flesh and blood. Sacrifice. The difference with the different rites is the point of balance between worship and sacrifice.