Narkissos.
Let me make some suggestions about the birth narratives.
Part of your argument hinges on the two-year delay for Herod to take action. You're assuming that Joseph and Mary would have remained in Bethlehem with Jesus until Herod decided to issue the decree. It certainly wouldn’t take two years for the Magi to travel from Bethlehem to Herod’s palace, so maybe your assumption is that the family had remained in Bethlehem some 18-22 months after the birth. I submit that need not be the case. Matthew does not indicate how long the family remained in Bethlehem, but I suggest it was only a short time. God would have known what Herod was going to do and warned Joseph early. Perhaps Herod forgot about the Magi for a while and something reminded him after a couple of years. This period MAY have included a delay between the time Herod decided to issue the decree and the time it would actually be implemented. In any case, I suggest the family was long gone by the time the soldiers arrived to carry out the order.
The other problem may lie with Luke writing that the family returned to Nazareth after the purification. On the surface, it seems to imply it was immediate, but again, no time period is specified. They simply ended up in , but did they go there directly, or by way of Egypt?
You suggest that the accounts of Matthew and Luke were written independently. I agree. I say it’s possible that the author of Matthew (the tax collector himself?) did not know that Joseph and Mary came from Galilee, or chose to ignore that, making it look as though they just haphazardly ended up there after coming back from Egypt.
Here’s another point: we aren’t told how long the stay in Egypt was.
The author of Luke, on the other hand, for all the research he did, may not have known about Egypt, or did not consider it relevant.
So a possible scenario: Joseph and Mary take the infant Jesus from Bethlehem after the visit by the Magi, stop in Jerusalem for the circumcision as good Jews would, continue on to Egypt, then return to Nazareth.