Your explanation doesn't work because Luke's genealogy is traced through Joseph. You are tkaing a reading that is not so much strained as directly contrary to the text. *If* you coudl show some precedent or some evidence to suggest that such a reading were at all plausible I would listen, but what you have is so weak that I would be reluctant to even class it as circumstantial evidence.
And no you haven't explained why Luke did not give Mary's lineage explicitly - you have invented an excuse. Without any precedent or any reason to think that it is remotely plausible that a lineage would be written in the fashion you claim.
It is not even as if Luke deliberately left clues - how much work would it take to give the name of Mary's father ? It's something that could quite naturally be included and while it would still only be a weak clue and inadequate to support your assertion it would have been far better than any of your "clues".
And yes I can give plausible reasons why Luke's Gospel states "He was the son of Joseph, SO IT WAS THOUGHT. . .?"
1) Only the paternal lineage counts so Joseph's lineage was given regardless
2) Luke copied the lineage from another source, but added the "SO IT WAS THOUGHT" to emphasise the Virgin Birth doctrine.
3) Luke did not write the "SO IT WAS THOUGHT", it was added early on because some readers were taking it as contradicitng the Virgin Birth doctrine.