That the two accounts do not harmonize presents difficulties to strict Biblical literalists and Sola Scriptura proponents is well understood. Some apologists conclude that the two genealogies for Jesus trace both his royal and his human lineage. Others find a way to show Mary's lineage. I personally have wrestled with it for years because, as Jesus did not have a human father, I am not settled on the context or relevance to the theories proposed.
The conundrum you are faced with, however, is that I, and Catholics in general, do not have a problem utilizing Tradition and other non-Biblical sources to assist in the interpretation of Scripture. Relying on the Jerusalem Talmud, which is nothing more than a collection of oral traditions, is doing the very thing that you condemn and belittle Catholics for doing.
So what I am really asking you is why you think you are better than any Catholic in Scriptural integrity and why you think http://gracethrufaith.com/ is better than a Magisterium?
Once again a misunderstanding, whether intentional or inadvertently I don’t know, of what Sola Scriptura means. Let me try this one more time.
Sola scriptura (Latin ablative, "by scripture alone") is the doctrine that the Bible contains all knowledge necessary for salvation and holiness. Consequently, sola scriptura demands that only those doctrines are to be admitted or confessed that are found directly within or indirectly by using valid logical deduction or valid deductive reasoning from scripture. However, sola scriptura is not a denial of other authorities governing Christian life and devotion. Rather, it simply demands that all other authorities are subordinate to, and are to be corrected by, the written word of God. [https://secure.wikimedia.org/wikipedia/en/wiki/Sola_scriptura]
By using the gracethrufaith site to explain what is in scripture in no way threatens the concept of Sola Scriptura. Prophesy states that Jesus would literally come from the line of David. The accounts in Matthew and Luke indeed show that Mary came through Nathan and Joseph came through Solomon but many fail to see it for some reason. Mary’s lineage through Nathan fulfills prophesy and agrees with scripture.
The Catholic doctrine of the assumption of Mary, purgatory, and others do not conform to scripture thus the difference.