Passover and the "New Covenant in My Blood"

I was thinking again recently about Jesus' institution of the Lord's Supper (read about it in Mark 14:22-25, Matt. 26:26-29, Luke 22:14-20; cf. 1 Cor. 11:23-26). What did he mean when he said "the new covenant in my blood" in the midst of him celebrating the Passover with his disciples? It seems to me that the Passover for the Jew is the remembrance of them becoming the people of God. It is the symbol of the exodus, and the preparation for Sinai. Even though the promise was to Abraham, it is the Passover the brings it to fruition. The Passover remembers how they were rescued out of slavery in Egypt, through the death of a firstborn lamb in the place of their firstborn sons, to be constituted the official new people of God in the covenant at Sinai. It seems that Jesus is saying that he is the reality of what the Passover pointed to. He is the lamb that was slain to rescue us from slavery to sin and the devil. And through his shed blood and death, we become the new people of God, united in the one body of Christ, after having been redeemed from the death that awaited us. In Christ we have become the new people of God, indeed the new humanity, united in him. It is the new covenant just as the Passover remembered what was then the new covenant as Abraham's physical descendants became the people of God. For some we can get caught up in the legalities of what it means to change from "old covenant" to "new covenant". But perhaps this misses the bigger picture emphasis of being one new people of God in Christ, through his blood shed for us (cf. 1 Cor. 10:16-17, Eph. 2:11-16). The challenge is how to live out that new unity as a true expression of new covenant life...