If the claim is that it was Mary instead who provided the bloodline link, what is the evidence for this, aside from conjecture surrounding the Lukan genealogy?
Great question, and I'm enjoying this discussion greatly!
Well, to this, I would say let's review the critical events in the geneology:
1. Abraham - David circa 1800 - 1000 BC (preserved in Gen-2 Sam)
2. David - Exile (Jehoiachin) circa 1000 - 586 BC (2 Sam - 2 Kings)
3. Exile, Return - Christ circa 586,539 - 0 BC (Ezra, Nehimiah, Matthew, Luke)
Just like when the world was destroyed in the flood and therefore the pre-Noah geneology is essentially irrelevant because HE becomes the common ancestor of everyone thereafter, Christ's geneology kind of bottlenecks at the Exile.
The returning Israelites would not have been that many, the whole assembly according to Ezra 2:64 42,360. That puts it at roughly 3,500 per tribe. Endogamy (marriage within the Israelite nation) is portrayed forcefully in Nehemiah, as he beats those who are of mixed descent. It seems to stem from this that even if it is Joseph's line chronicled in both that Mary would not have been far from Joseph in the family tree. Marriage between cousins was common as was marriage between uncle and niece. Admittedly, there is an element of faith in this, as in anything, but it seems to logically flow this way as well.
And a brief aside that you aren't going to like...
While I tend to believe that the Lukan geneology is Mary's, if you look at the line and the people in it such as Rahab the prostitute, David the adulterer (though great King as well), Tamar (look that one up in Genesis, too sordid to briefly recount), Ahaz the 'wicked' king of Israel, etc... God clearly uses people who would not fit the profile of a "righteous" line to deliver forth his Son. Therefore, it may be that God fulfills the prophecy through Joseph, in a way that most people wouldn't see or accept, as the way He works is clearly never quite what we're thinking...
God Bless.