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.