What an interesting response. Thank you for sharing.
There are so many issues so I suggest you focus on one and hang onto it like a dog with a bone.
If it were me, I would focus on their "year 537 B.C.E., the Jewish remnant had returned to populate once again Jerusalem and the land of Judah".
Previously, they had pointed to the 7th month when Returnees gathered at the temple site, some time after returning from Babylon. (7th month is about October, hence they pointed to October 1914). Note that Jerusalem was destroyed in the 5th month (about August).
Ask them how they can guarantee the returnees arrived in 537 BCE. There is no universal agreement on the year, ranging from 538 BCE to as late as 535 BCE. Keep it simple and do not let them slip around like a wriggling snake.
Doug