This stuff is the doctrinal equivalent to the cat on the keyboard. It's why confusion reigns. The experts who come up with all these weird schemes are like the pols who pass laws "for the people", knowing and intending that their laws (doctrines) will create new problems for them to $olve. GOPe or GODe, same thing. The Establishment is a house built upon sand.
The structure of Elohim and elementary particles appears to derives from the Universe starting as three books, or spheres, a long time ago. It is based on the natural numbers, which require twelve axioms to define them. All this is captured in the Three Patriarchs and the 12 Sons of Israel. Grouping the Sons of Israel by their birth mothers in their birth order, we get the organization of the 12 dimensions of the Universe. But that is for another time and another book.
Or another (bigger) transfer station. Of making many books there is no end.
Jesus had two lineages from David. A legal one through his adopted father, and a genetic one through his mother. The matriarchal linage is important because Sin entered the world through the male, Adam's, line. So to be born sinless, Jesus had to have the Holy Spirit as his father.
Tribal lineage/heir to the throne = patrilineal descent. Joseph = son of David. Sarah was ninety; Elizabeth was also "too old", so some sort of intervention into the normal system was required to bring forth a child. Not a big deal then with a virgin birth and Joseph-as-father being simultaneously true. Medical science succeeded with a secular method back in 1978.
So to be born sinless, Jesus had to have the Holy Spirit as his father.
David and Paul had the right concept. (e.g. Psalm 32, 51; Romans 4)
Nothing amiss with the genealogies as-is. [Son] of God through David via Nathan. That is, the character and heart and soul of David. Solomon turned his heart away. His heart wasn't perfect with God as was David's.
The very next chapter in Luke starts off with Jesus spirited off to the wilderness, and being addressed as the Son of God. Having the heart of his father David, he didn't get tripped up by the devil's appeal to ego.
Matthew's genealogy [with a "begat" after every father's name] runs forward from Abraham to David through Solomon to Joseph. No "begat" with Joseph's name, because technically there was a different method. No sloppiness with the details, but let the experts get in there and out comes a man-god. Hence no library is big enough to contain all their writings. Like deciphering Obamacare - just have to take it on faith.
Son of God = heart (character) of God = heart of David = Son of David = spiritual heir to the throne (embodiment of Torah - the perfect king, judging righteous judgment)
Son of Man = "human being" = physical (patrilineal) descent from David through Solomon = physical heir to the throne
Joseph son of David was a merciful and a righteous man like his father David, intending to quietly deal with Mary's seeming transgression. He had to be informed in a dream that all was well, but he didn't need the dream to be kind and loving. It came naturally. His son also.
Amazing what gets missed when Joseph *son of David* is relegated to obscurity as a token head of household.
In any case, all the above resolves down to the simple meaning:
Matthew 22:34-40
34 But when the Pharisees had heard that he had put the Sadducees to silence, they were gathered together.
35 Then one of them, which was a lawyer, asked him a question, tempting him, and saying,
36 Master, which is the great commandment in the law?
37 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind.
38 This is the first and great commandment.
39 And the second is like unto it, Thou shalt love thy neighbour as thyself.
40 On these two commandments hang all the law and the prophets.
David had it right down to the basics. Poured his heart out. Praised God for His mercy and loving kindness. The character of God was his template. His soul was his livelihood; his livelihood his soul. David wanted to get things just right, which meant knowing that God desires mercy not sacrifice, knowledge of God more than burnt offerings. No wonder the Messiah is the son (embodiment) of David. No wonder the experts didn't recognize him. No wonder history will repeat.
Ezekiel, I read you comments, and I looked at your home page. It looks to me as if you are going to be OK, but just to be sure:
Romans 10
8 But what does it say? The word is near you, in your mouth and in your heart (that is, the word of faith which we preach):
9 that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved.
10 For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation.
11 For the Scripture says, Whoever believes on Him will not be put to shame.
12 For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him.
Nelson, Thomas (2009-02-18). Holy Bible, New King James Version (NKJV) (p. 1100). Thomas Nelson. Kindle Edition.