This really is a mouthful. It may be helpful to remember Paul's comment that God gives life to the dead and calls those things which do not exist as though they did (Romans 4:17), because the imagery in these verses blends the present and future together. But my focus is on the phrase, the spirits of just [or, righteous] men made perfect, and its connection to the Covenant. This is what the New Covenant does. Having God as our God, and knowing Him, and having His laws put into our minds and written on our hearts, leads to perfection.
Thus, the blood of the covenant - the blood of the Savior - is a symbol, a pledge, of God's purpose to perfect us. In this also we see that Passover speaks to something that is ongoing, something set in motion by Christ's death. When we are resurrected, immortal beings, we will be completely redeemed from this life in the flesh, not only with new spirit bodies, but more importantly, with a nature just like God's. When we are perfect, then Passover will be fulfilled, which is why Jesus put the fulfillment in the Kingdom.
The blood of the New Covenant is not sprinkled on the outside of those making the covenant, as was done with Israel. Instead, it is ingested. It goes into the innermost parts of the person. It is a covenant that changes us on the inside, nor merely covering us on the outside. Instead of being sealed with the blood of oxen, the New Covenant is sealed with infinitely more precious blood, blood that serves as a testimony of eternal life (see I John 5:6-12), as well as a pledge of God's loyalty to those within the covenant (see I Corinthians 11:25; Hebrews 10:29; 12:24).
