1. Question Restatement:
How could Jesus justify directing people to "Drink his blood" - even figuratively - when even David refused to do it, in a figurative sense, and given the Biblical commandment to not drink blood?
In legal texts, qualifications and distinctions matter - a lot. And there is an incredible difference between a prohibition against neglecting to remember the horror of taking life from unwilling sacrifices - and the requirement against the horror of failing to remember the life freely given, by a willing sacrifice.
This distinction is more than enough, legally - under Rabbinic reasoning - especially Kal va-chomer (קל וחומר) - and the ability to navigate child sacrifice.
Remember - the prohibitions in the Old Testament were against blood AND fat, (Leviticus 3:17), which I am not even sure was remotely possible for them to do. The intent of the command was explicitly metaphorical - but to be observed literally, in order to be mindful of the value of life.
If a person were to presumptuously demand, and then take personal advantage of, another's sacrifice - that is morally wrong.
On the other hand, if a person was making a self-sacrifice, on behalf of others, and asked others to "remember this" - but they didn't - this would be morally wrong.
2.1. The Mosaic Explanation of the Metaphor:
Going back to the commandment, this commandment is actually based on this exact moral value - as metaphor; and because Israel had refused to act morally, the prohibition had to be enacted by statute.
NASB, Leviticus 17:11 - For the life of the flesh is in the blood, and I have given it to you on the altar to make atonement for your souls; for it is the blood - by reason - of the life that makes atonement.’
2.2. The Christian Explanation of the Metaphor:
For Christians, every commandment given to Israel was in prophetic view of what the Messiah was to do and teach.
NKJV, Luke 24:25-27 - 25 Then He said to them, “O foolish ones, and slow of heart to believe in all that the prophets have spoken! 26 Ought not the Christ to have suffered these things and to enter into His glory?” 27 And beginning at Moses and all the Prophets, He expounded to them in all the Scriptures the things concerning Himself.
So, How Does this Self-Sacrifice Result in Atonement?
It doesn't, and never will. God never delighted in sacrifice, or death, ever, and never will. God desires mercy. It was Jesus' unconditional advocacy for mercy proven by the extent of his self-sacrifice, that brought life.
NASB, Philippians 2:8 - Being found in appearance as a man, He humbled Himself by becoming obedient[for mercy] to the point of death, even death on a cross.
There are way to many examples of this to list here, but: Moses' advocacy to spare the nation of Israel, David's advocacy on the threshing floor, Rahab's self-sacrifice for "spies/terrorists" bringing life to Israel, Job sacrificing and praying for his friends - resulting in Job's own healing, Eve advocating for Adam - resulting in the verdict of death being overruled, Esther, Jonah having to advocate for Nineveh, (of all places), Noah for his family, etc., etc., etc.
That is a whole lot of "wrong" and "sinful" people making a way for God to show mercy, through advocacy alone - even when they were wrong.
A Paraphrase of Many Passages about "Blood" and "Sacrifice":
Rephrase: It is morally reprehensible to neglect that "giving one's life" is the greatest sacrifice that anyone can make - because "life" is the greatest gift that God has given:
Paraphrase: God desires life - not death(Ezekiel 18:32), mercy and not sacrifice(Hosea 6:6). So, because you are as children and not mature, you will be given statutes(Galatians 3:24), until this is a natural inclination of your heart(Jer. 31:33). So, you are required, by law, to remember that "blood" represents "life"(Gen 9:4) every time an animal is sacrificed for you - by not eating its blood(Lev. 3:17). You and your children will only find abundant life(Deut 12:23) by remembering(Luke 22:14) that only by following the greatest commandment to love, by imitating(John 15:12) unconditional advocacy(Isaiah 53:7) for life and mercy, will a multitude of sin be covered(1 Peter 4:8). Because, mercy triumphs over judgment, and judgment will be merciless to those who show no mercy(James 2:13).
Note: This is kind of turned out as a paraphrase of the entire Bible.
This answer is obviously not accepted by "Judaism" - but requires a fundamental "change of mind" regarding "mercy and punishment". If that value is indeed true - then Jesus' requirement to remember mercy, through metaphor, is perfectly valid - especially since real blood isn't being drank anyway.