Jesus - the Lineage

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Matthew and Luke present different genealogies of Jesus--one through David's son Solomon (the royal line) and the other through David's son Nathan (the non-royal line). The royal line is traced in Matthew; the "natural" line in Luke. Matthew's genealogy goes only back to Abraham (to show the Jewish character of the King); Luke's goes back to Adam (to show the universal aspect of the Savior). Matthew's emphasizes Jesus' royalty; Luke, his humanity.
It is generally accepted (but not unanimously) that the genealogy in Matthew belongs to Joseph's family, and the one in Luke applies to Mary's line. (The historical evidence is fairly strong that both Mary and Joseph were of the house of David.)
Both genealogies are 'aware' of the virgin birth: Luke adds the phrase "He was the son, SO IT WAS THOUGHT, of Joseph" (3:23) and Matthew switches verbs from "X begat Y" to "Joseph, the husband of Mary, of whom (feminine pronoun) was born Jesus".
So, how does Joseph 'step into' Mary's lineage? How does he 'pick up' her legal heritage?Probably through the law of levirate marriage.The Jewish folk had numerous provisions for cases of inheritance-transfer in extreme cases. One of the more frequent situations that had to be covered (in a land-based, clan-ownership system) was that of childless marriages, or in some cases, of son-less marriages.
One of the more concise statements of how this would apply here, is by J. Stafford Wright in Dict. of New Test. Theol., III. 662:"Mary's father (Heli?) had two daughters, May and the unnamed wife of Zebedee (John 19:25; Matt 27:56). If there were no sons, Joseph would become son of Heli on his marriage, to preserve the family name and inheritance (cf. Num 27:1-11; 36:1-12, esp. v. 8, which accounts for Mary marrying a man of the family of David.)"
[The main passages in the OT that refer to these various laws are Num 7:1-11; Num 36:1-12; Lev 25:25; Dt 25:5-10. These practices were widespread in the Ancient Near East, and a good discussion of the details in Israel and differences from the ANE can be found in Roland de Vaux, Ancient Israel: Vol 1--Social Institutions. Two famous cases, for good or ill, of these practices are in the story of Ruth (Book of Ruth) and in the story of Tamar (Gen 38:6ff).]
What this 'nets out to' is that Joseph 'married into' Mary's gene-pool...and hence, the virgin birth doesn't stop the lineage "transfer".In other words, the the physical-gene did NOT come FROM JOSEPH was IRRELEVANT in this case. Legal standing was related to EITHER 'genes' OR to 'marriage'. (Although it should be pointed out that levirate arrangements like this required close kinship already, and hence, quite a number of overlapping genes.).So, strictly speaking, Jesus got his genes from Mary and his legal standing (in the royal heir line) from Joseph (thru the marriage of M+J).
Now, as a practical matter, I consider the gene-issue to be important, simply because there were NUMEROUS other indications that the Messiah WOULD BE from the 'stock of Jesse' etc--images and phrases that DO put more emphasis on the blood-line that does simply 'legal lineage'--but I am persuaded that these requirements were adequately satisfied from Mary's side.

The historical evidence is fairly strong that both Mary and Joseph were of the house of David.

Is there historical evidence that these people even existed?