I've already explained why Heli is the Father of Mary. That combined with my hunch that the solution to the Kenen issue is that Kenen was Selah's older brother by some 15 or so years and Selah married Kenen's daughter. Leads me to conclude that Luke 3's genealogy sometimes records the descent through a woman, but keeps it patriarchaly expressed by listing the woman's husband as the son in law of her father. Joseph is distinct though because he is the only one who is NOT a biological ancestor of Jesus, thus he alone lacking the Greek definite article.
This can also explain the issue regarding the father of Shealtiel. I think a daughter of Neri married Shealtiel son of Jechoniah, then he died without an heir and so she married his brother Pedaiah and had Zerubabbel.
So my theory is when Heli is called a Son of Matthat it could mean son in law. And so on.
An interesting name in Luke 3:24 is Janna. Janna is a rare name, and the only recorded example of the name around the time this Janna would have lived is the Hasmonean King Alexander Jannaeus. Again I suspect the Joseph he's described as the son of could be his wife's father.
The only known wife of Alexander Jannaeus was Queen Salome Alexandra (Shelomtzion or Shlom Tzion). Josephus tells us nothing about her family, but rabbinic traditions recorded in the Talmud say she was the sister of Simeon bar Shetah. Simeon's father was Shetah bar Yossei. Since the Talmud is oral traditions written down at least 200 years after Salome's time, it could be the nature of her relation to this family had slipped by a generation, and Simeon was her nephew and Shetah her brother. Since Yossei is a different form of Joseph, that would make Alexander Jannaeus a son in law of a Joseph.
This family was one of the leading families of the Sanhedrin, from what I know about other leading families of the Sanhedrin (like the House of Hilel which came later), they often had Davidic ancestry. And once the Hasmoneans started ruling as Kings it would make sense they'd want to marry into the House of David. So Yossei being a descendant of Nathan Ben David is reasonably plausible.
Salome and Jannaeus had two sons, Hyrcanus II and Aristoblus II. From then on with few exceptions all the Hasmoneans are known only by Greek names, but I suspect most also had Hebrew names too.
But Melchi may not even be the main Hebrew name of whoever is meant, it derives from the Hebrew word for King. Both sons had been Kings, though there are reasons, given what happened, why I feel Aristobulus II was more likely to have used Melek as an alternate name.
Aristobulus II had two sons and two daughters one of whom was named Alexandra (not to be confused with the Alexandra who married her brother Alexander). Himself, his son Matthias Antigonus II, and his daughters are recorded as being taken to Rome by Pompey after he captured Jerusalem in 63 BC, Josephus Antiquities of The Jews Book 14 Chapter 4, at the end of the chapter. They later returned to Judea, after the death of Aristobulus II in 48 BC they were protected by Ptolemy Bar Mennaeus according to Antiquities Book 14 Chapter 7, at the very end. Phillipon the son of Ptolemy married Alexandra, but later Ptolemy killed him and married Alexandra. The unnamed daughter after Antigonus died held the Hyrcania Fortress till just before Actium in 31 BC.
I suspect the unnamed sister is more likely to have possibly been married to a Levi.
Robert Graves started a fringe theory that involved Matthias Antigonus II as the Matthat of Luke 3:24 (a theory defended in a book called Herodian Messiah). His scheme however did not match a strict literal interpretation of Scripture and so I do not intend to support it specifically at all.
Janna was a rare name which is why I think it could be significant. Matthat/Matthias/Matthew was very common however, so that's not as significant. Still hypothetically if this Matthat was Antigonus II, we know pater-lineally only one generation comes between him and Jannaeus, so it would mean he married either his niece or a first cousin once removed. Neither of which are included in The Bible's incest restrictions, so it would be perfectly legal.
In John 8:48 Jesus is accused of being both a Samaritan and Demon Possessed, he denies being Demon Possessed but not being a Samaritan.
I talked in the Heli post about why Heli could be an alternate name for a Jehoiakim, and how Jehoiakim was in some traditions the father of Mary. Jehoiakim is also a fairly rare name, so it's interesting that the Samaritan records claim a Jehoiakim was their High-Priest at about this very time period, (number 38).
That connection is a tenuous one however. But Matthias Antigonus is known to have had at least one daughter.
The Herodian Messiah theory alluded to above is dependent on confusing the two wives of Antipater. Mariamne III who was a daughter of Aristobulus IV, and an unnamed wife who was a daughter of Matthias Antigonus. The Herodian Messiah theory makes Antipater the wife of Mary and father of Jesus. My theory makes a daughter of Antigonus possibly Mary's mother, not Mary herself.
I've actually expressed elsewhere my suspicion that the claims of Herod being an Idumean may have been propaganda against him. Though his official claim to Exilarch descent is also very likely to be propaganda. I certainly reject the assumption that the Idumeans were Edomite, I view them as Ishmaelite (with a possible Simeonite element), and Antipater did have Idumean descent through his mother. The relationship between Herod and Costobarus suggests to me that Herod didn't think of himself as Idumean at all.
Antipater is a Greek name, so Antipater son of Herod could have had an additional Hebrew or Aramaic name that history hasn't recorded.
It's possible this woman wasn't the only daughter of Antigonus II. And it's also possible she was already a widow when she was married to Antipater, if Antigonus himself had ever arranged a marriage for her it wouldn't be likely to have been to a Herodian.
I think one factor in why Luke laid out this genealogy how he did was because of the potential significance in the numbers. Luke's genealogy has Jesus as the 77th from Adam and 70th from Enoch.