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Another answer by George Calvas:

The line from David to the carrying away to Babylon is "incomplete"
and therefore the "all" the Lord is talking about are "all" he is
concerned about! The word "all" does not necessarily imply EVERY
SINGLE genereation (ex: And there went out unto him ALL the land of
Judaea, and they of Jerusalem, and were ALL baptized of him in the
river of Jordan, confessing their sins). Therefore, the INTERESTING
aspect is to know why between Joram(Jehoram) who it says begat Ozias
(Uzziah), three kings were not mentioned (there was Athaliah [2 Ki
11:3]who reigned as the mother of Ahaziah, but not to be included
as "the seed"). Also you must note that between Josias (Josiah) and
Jechonias (Jeconiah), two kings are missing, Jehoahaz (2 Ki 23:31)
and Jehoiakim (2 Ki 23:36). Those two were actually the sons of
Josiah, while Jeconiah was the son of Jehoiakim (Josiah's grandson).
I am not sure what that all means, but 3 times 14 (7 x 2) generations
are mentioned. I personally do not see any problem at all. Maybe it
was that the connection of the number 14 offered some proof
concerning the accuracy of this reckoning of the geneologies?

The line from David to the carrying away to Babylon is "incomplete" and therefore the "all" the Lord is talking about are "all" he is concerned about!

Indeed. I am in complete agreement. I'm curious though, why do you think Thayer specifically says that the use of the word "genea (1074)" should be taken as "successive", in that particular verse?

It's just a point of curiousity for me anymore now, and not a source of doubt as it was during the last week.

Thanks again for your posts! They've been very helpful.

God Bless,