So how do you explain the sacrifice of “good works” that Paul talked about; or the sacrifice of a “broken and contrite heart” that Psalms 51:17 talks about?
Those two examples each have their own contexts. It so happens that in Heb 13 Paul is using a lot of liturgical language. I barely started to explain it all in my post. For instance, even the word he uses for “approach” in this chapter has a liturgical connotation. And in the verse you quoted, Paul is using a technical term that denotes a specific rubric of liturgical sacrifice. So I follow that context and interpret it in that light.
As for Ps 51:17, I’m not sure why you would think it is a problem verse unless you are thinking of it as a
carte blanche statement that God doesn’t care for sacrifices. It would be hard to apply such a principle throughout scripture consistently, since God commands sacrifices, and Christ himself achieves salvation through a high-priestly sacrifice. Moreover, Hebrews makes its case for the new sacrifice by pointing to the deficiencies of the sacrifices in the Old Law. So a Psalm that points to those deficiencies as well does not at once suggest a problem, but rather a point of basic agreement with the core premise that Hebrews to show the power of the new sacrifice of praise.
Let’s look at the particulars of the psalm. Here David is deeply aware of his sins, and is asking the Lord to deliver him. His sins are grave and include “bloodguiltiness,” presumably for the murder of Uriah. Before God can be appeased by any sacrifice, David’s heart must be contrite and penitent, since God does not accepts sacrifices done without love. In order to be appropriately cleansed, David asks God to “Purge me with hyssop.” (Ps. 51:7) Now hyssop branches are a tool of priestly, sacrificial service, and Hebrews 9:18-22 indicates its use in purging sin through liturgical blood-offering:
Whereupon neither the first testament [actually “covenant”] was dedicated without blood. For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people, saying, This is the blood of the testament [covenant] which God hath enjoined unto you. Moreover he sprinkled with blood both the tabernacle, and all the vessels of the ministry. And almost all things are by the law purged with blood; and without shedding of blood is no remission.
By asking to be purged with hyssop by God, David is acknowledging that his sins *can *be atoned by blood sacrifice, just not by any sacrifice that he can offer. Any efficacious sacrifice has power only by virtue of the cleansing that comes from God, so that the sacrifice of a pure heart creates the condition that makes the ritual sacrifices of the Old Law meritorious. David’s sacrifice of a pure heart is nothing other that his reception of the cleansing sacrifice that God provides.
David’s words, therefore, long for Christ who is that very sacrifice. Jesus had a hyssop branch placed to his mouth (John 19:29) and he uses that same words as Moses when instituting the Eucharist:
“This cup is the new testament [covenant] in my blood…” (Luke 22:20; 1 Cor 11:25). The sacrifice of Jesus provides the cleansing that David seeks. Just as the blood sprinkled by Moses was sacrificial blood, Jesus is indicating that the cup also contains sacrificial blood. The hyssop branch connects all these passages together.
As for the sacrifice of good works, I do not know what particular verse you have in mind, but clearly, Paul does see an upright life lived in charity as a sacrifice to God. Of course it is. That does not negate the validity of liturgical sacrifice. Why would it?