How else should one deal with them? The Gospels themselves show two different dates. The history of Quirinius is well known. And the Gospel of Luke specifically names him and the census that he ran. There are also several independent lines of evidence that show that was the first census of Judea under Rome. The main reason is that Judea was not part of Rome before 6 CE. It was not part of the empire. It was a client kingdom, which meant that it was a close ally to Rome, but would mainly have existed as a buffer against possible attacks upon Rome. They would not have been taxed. Second we know that censuses used to be illegal in Judea. In fact ever since the time of David. You should read your Bible some day to see why. There was a minor revolt in 6 CE due to this "illegal" census. At least that is how some of the population saw it. The names of the leadership are known. Censuses, especially ones for taxation purposes, always count people where they live. It would have been insanely idiotic to require them "return to an ancestral home". Worse yet, Nazareth was not part of Judea at that time. Herod split his country into four parts when he died. That part was not taken over by Rome, the people that lived there would not have been counted in a census since that was still a client kingdom and not part of the empire.
The reasons how and why the story fail are overwhelming. The evidence for it? A book that is largely filled with myths and legends. You need something a lot stronger than that.