The serious dilemma of Jesus genealogy

The Holy Gospel of Matthew alleges that Yeshua (Jesus of Nazareth, peace and blessings be upon him), was a direct descendant of King David. Why? Well, because, according to Matthew, Joseph [Yeshua’s putative] was a descendant of King Solomon (that is, of a legitimate heir to David’s throne).
As it is written: «BOOK OF THE GENEALOGY OF JESUS CHRIST, SON OF DAVID, son of Abraham. Abraham fathered Isaac, Isaac fathered Jacob, and Jacob fathered Judah and his brothers… Jesse fathered King David, and KING DAVID fathered SOLOMON…. Eliud fathered Eleazar, Eleazar fathered Matthan, Matthan fathered Jacob; AND JACOB BECAME JOSEPH, THE HUSBAND OF MARY, OF WHOM WAS BORN JESUS, who is called the Christ»- Matthew 1: 1-16.
But the holy Gospel of Luke denies the genealogy given by Matthew; for it asserts that Joseph was not a direct descendant of Solomon (the legitimate heir to David’s throne), but that he was instead the descendant of an illegitimate heir. Who was this illegitimate heir? Could it be Jonathan? Was it Adonijah? Nope! Joseph's alleged ancestor was Nathan, a son of David of whom Scripture never records that he held the royal chair. As it is written:
“JESUS HIMSELF AT THE BEGINNING OF HIS MINISTRY WAS ABOUT THIRTY YEARS OF AGE, THE SON, ACCORDING TO BELIEVED, OF JOSEPH, son of Eli, son of Mattath, son of Levi, son of Melchi, son of Hana, son of Joseph, son of Mattathias, son of Amos… son of Melea, son of Menna, son of Mattatha, son of Nathan, son of David, son of Jesse, son of Obed…”- Luke 3: 23-32.
Obviously, Joseph could not be a direct descendant of two different sons of David- Either he was a descendant of Solomon, or was he a descendant of Nathan; but under no circumstance can he be a direct descendant of both men.
So this is one of those cases where there is no doubt that one of the two gospels is making a serious mistake.
But if one of the two gospels is wrong, then there's also a chance that both gospels are wrong. And how do we know that the latter is the case? Well, we know it because from the fact that the gospels claims Jesus wasn’t Joseph's biological son [he was instead son of God! ]. And, if so, then Joseph’s [alleged] Davidic ancestry is irrelevant; as it could not be used as evidence for Yeshua’s royal ancestry.
In fact, according to God’s Law, the Nazarene (peace be upon him) was technically a bastard. Why? Simply because he wasn’t the biological son of his mother's legal husband. And the Law not only prevented such persons from aspiring to David’s throne, but even from becoming part of Israel's congregation [which in practice meant Jesus couldn’t marry any female Israelite-- something the gospel seems to confirm]. As it is written:
“NO BASTARD SHALL ENTER THE CONGREGATION OF ADONAI YAH; not even to the tenth generation shall they enter into the congregation of Adonai Yah”- Deut. 23: 2.
Does what has been exposed here mean that the Nazarene (Christian) faith is false? Does it mean that faith in Yeshua is incapable of transforming a life for good-- thereby bringing it closer to the Creator? Of course not! It simply means that, although a perfectly valid path to serve the Creator, Christianity's theological foundation doesn't perfectly agree with the things revealed by God to Israel.
In other words, Christianity is one of several Divine approved paths given to the gentile nations; but it isn’t the path of Torah compliance entrusted by God to the people of Israel. As it is written:

1) “So shall I keep thy Law continually for ever and ever. And I will walk at liberty: for I seek thy precepts”- Psalm 119: 44-45 (King James Bible).
2) “... Hear, O Israel, the statutes and judgments which I speak in your ears this day, that ye may learn them, and keep, and do them”- Deut. 5: 1
3) “Thou hast commanded us to keep thy precepts diligently”- Psalm 119: 4
4) “ With my whole heart have I sought thee: O let me not wander from thy commandments”- Psalm 119: 10.
5) “I am a companion of all them that fear thee, and of them that keep thy precepts”- Psalm 119: 63
6) “ The wicked have laid a snare for me: yet I erred not from thy precepts”- Psalm 119: 110
7) “And the Lord said unto Moses, How long refuse ye to keep my commandments and my Laws? ”- Exodus 16: 28
8) “Thou hast rebuked the proud that are cursed, which do err from thy commandments”- Psalm 119: 21.
9) “O that there were such an heart in them, that they would fear me, and keep all my commandments always, that it might be well with them, and with their children for ever! ”- Deut. 5: 29
10) “This day the Lord thy God hath commanded thee to do these statutes and judgments: thou shalt therefore keep and do them with all thine heart, and with all thy soul. Thou hast avouched the Lord this day to be thy God, and to walk in his ways, and to keep his statutes, and his commandments, and his judgments, and to hearken unto his voice: And the Lord hath avouched thee this day to be his peculiar people, as he hath promised thee, and that thou shouldest keep all his commandments; And to make thee high above all nations which he hath made, in praise, and in name, and in honour; and that thou mayest be an holy people unto the Lord thy God, as he hath spoken" - Deut. 26: 16-19.