Which Bethlehem?

According to Matthew 2:1 and Luke 2:4-7, Jesus was born in Bethlehem in Judea – about 6 miles south of Jerusalem.
However, Israeli archaeologist Aviram Oshri surmised that Jesus was born, not in Bethlehem of Judea, but in Bethlehem of Galilee.
It is certainly not news that there were two Bethlehems – one in Judea and the other in Galilee. The latter is mentioned in Josh 19:15.
As reported in this article in The Times of Israel, Oshri asks:
‘How would a woman who is nine months pregnant travel 175 kilometers on a donkey all the way to Bethlehem of Judea? It makes much more sense that she would have traveled seven kilometers’ (the distance from Nazareth to Bethlehem of Galilee).
The alert reader will already spot some flaws in Oshri’s argument. The biblical text makes no mention of a donkey, and nowhere says that Mary was ‘nine months pregnant’! Concerning the latter point, we are simply told that she was pregnant and that she gave birth while she and Joseph were in Bethlehem (not soon after they arrived).
Moreover, a birth in Bethlehem of Galilee does not remove the ‘problem’ of distance – it only shifts it slightly. For, if it is implausible that Mary would travel the 175km while pregnant, it is, if anything, yet more implausible that she and Joseph would travel that distance with an 8-day old baby (in order to visit the Temple in Jerusalem)! A similar problem applies to the last stage of the Magi’s journey: according to Mt 2:8 they were directed to Bethlehem of Judea; a journey to Bethelehem in Galilee would involve an implausibly long journey (to say nothing of flatly contradicting the biblical text).
The only real question is whether either or both towns were occupied at the time of Jesus’ birth. Oshri states that no archaeological remains from the Herodian period exist at the Judean site. But the adage that ‘absence of evidence is not evidence of absence’ is particularly true in the field of archaeology. According to the HarperCollins Bible Dictionary, little archaeological activity has been possible there because of the presence of the modern town.
According to this article, no ancient source ever associates Jesus’ birthplace with anywhere other than Bethlehem of Judea. As early as the 2nd century AD Justin Martyr identified the cave beneath the Church of the Nativity in Bethlehem of Judea. It is difficult to account for this if it is not based on a still earlier, and reliable, tradition.