I’ve nothing to add (good job BTW

) to what you wrote, but I’ll point out something interesting regarding the genealogies.
You would notice that Matthew’s genealogy traces Jesus’ lineage back to Solomon (thereby establishing Him as a legitimate heir of the royal Davidic line - a King in a long line of kings), while Luke’s links Him to David via another son, Nathan. As you can notice, by linking Him with the
other, non-royal Davidic line, Luke
avoids connecting Jesus with the kings of Judah - that very same line which (save for a few bright spots) generally fell from grace by indulging in false worship. It would seem that Luke has taken the prophecy of Isaiah (“There shall come forth a shoot from the stump of Jesse, and a branch from his roots shall bear fruit”; 11:1) and understood the reference to “the stump of Jesse” as meaning that the tree of the Judahite monarchy, the Solomonic line, had failed - was cut down - because of their unfaithfulness to God. For Luke, there will be a new beginning: a new shoot - a more faithful line - will instead replace that unfaithful lineage of corrupt and idolatrous kings. So he connect Jesus to Jesse and David not through Solomon, but through Nathan.