Let me describe the way I take part in the Mass. The other priests who say Mass where I do usually put an extra cross on the altar before them to help them realize they are taking part in the sacrifice of Good Friday. I don’t go along with that because I prefer meditating on how the Mass is rooted in the Last Supper.
Our English version of the words written by Matthew, Mark, Luke and Paul quote them as recalling Jesus saying, “This is my body which will be given for you.” They picture him as looking forward to his death the next day. However, in the actual Greek wording of Matthew, Mark, Luke and Paul, Jesus said, “This is my body which is given for you.” Taking it that way, I imagine he was already giving his life at the Last Supper.
Another thing. Those three wrote that Jesus “said the blessing.” We usually take that to mean he said two or three appropriate words. However there was a three-part ritual blessing that was proper to that formal dinner. By that blessing Jesus first asked the diners to join him in recalling God’s many favors. Secondly, he asked them to join him in begging for God’s Spirit. Thirdly, he asked them to join him in becoming part of a Pleasing Gift to God. They would do that by offering complete obedience to God’s will.
Now, I think he might have chosen that time to give himself to them in order that they could be one with him in the same Pleasing Gift. The Greek for Pleasing Gift, the third part of the blessing, was Eu-charis.