It is my great joy to draw your attention to this journal article by Jared M. Compton who does a thorough job of summarizing current scholarship on Luke's dubious reference to the Roman Proconsul Publius Sulpicius Quirinius. (H/T Charles Savelle at Bible X) For those most interested, I recommend printing the whole page, because the footnotes are twice as long as the arguments. Anyone unfamiliar with the problem can follow the author's footnotes, which are comprehensive for all major relevant opinions on the issue.
The article's conclusion takes a straightforward reading of Luke 2:2 and posits that Quirinius held an "otherwise unattested office" under some Syrian Legate prior to 4 BC. For grammatical reasons I couldn't sum up if I wanted to, Compton prefers this to the solution of F.F. Bruce, Harold Hoehner and others (that Luke 2:2 refers to the census "before" Quirinius was Governor). Personally, I still prefer a strained syntax over inventing history, but I have to admit it is plausible and it does make more curious to learn more about Luke's grammar. To Compton's credit, if his arguments about grammar are solid, the posited solution is probably necessary.
In the end, I'm thrilled about Compton's argument because - imho - the article successfully demonstrated that (1) the best explanations for Luke 2:2 all favor a birth date for Jesus before 4 BC and (2) in every explanation, Luke 2:2 offers no further help in pinpointing that date, chronologically. This is correct and needs to be acknowledged more often.
Therefore, whether we take the solution of Bruce and Hoehner or the one suggested by Compton, Luke 2:2 should no longer dominate or inhibit historical investigation about this Luke-attested registration that occurred under Augustus and Herod the Great.