This blog has had some occasion to look into The Third Gospel's use of material and into its general tendency. Some of Luke's changes can be illustrated with textual-strain. Among the more-diverting results is Jesus' long gestation: he was conceived in Herod's reign (d. 4 BC) as in Matthew, but he came out among us during Quirinius' census (r. AD 6). Mary bore a burden quite unlike those of most women.
Miracles, or snark, aside: at least Joslin McDowell never entertained that notion, Protestant as he is (yeah, he's still alive). He prefers that Quirinius was there several years before. And maybe this Roman was; but he wasn't doing census in someone else's kingdom. Especially not Herod's.
Michael Kochenash explains Luke's plan. Luke knew of Roman-Jewish talk that the census was a flashpoint of rebellion, and this rebellion in particular. Kochenash goes further: he notes Josephus (a Galilean friend of Herod Agrippa II) in The Jewish War and Antiquities. The former, Josephus completed before the Campanian volcano buried Agrippa's sister; this eruption received note only in the latter.
TJW is well aware of Quirinius' census and of the revolts around it. But this book does not connect those events with the Revolt. The connexion becomes explicit only in JA. Kochenash does not see Josephus, here, arguing that point for or against other historians like Justus. It seems an idea that Josephus had just... come up with. A reasonable idea, to my mind anyway; but never mind that.
Kochenash does not think that Saint Luke had come up with that idea, either, by himself. Instead - Kochenash argues - Luke made of it a trope. Roma and Judaea came into serious Imperial contact through that census. Luke associates this contact with Jesus' infancy. What the Jews do to Jesus, is going to post a milestone to the Ninth Of Av; which the Jews perhaps could have averted, by embracing him as Christ.
Crossan would supplement, here, the Holy Spirit as Divine gloría. This has abandoned the Jews to settle upon the Apostles, and - finally - upon Peter and Paul who are headed westward.