Your dating is wrong. In addition...
And curiously enough, even if that were NOT the case somehow, the linguistic data of the last few decades indicates that Luke 2.1 should be translated 'BEFORE the census of Quirinius' instead of the customary 'FIRST census of Quirinius'--see Nigel Turner, Grammatical Insights into the New Testament, T&T Clark: 1966, pp. 23,24 and Syntax, p. 32. This would 'solve the problem' without even requiring two terms of office for Q.
And, while we are talking about Greek here...the term Luke uses for Quirinius' 'governorship' is the VERY general term hegemon, which in extra-biblical Greek was applied to prefects, provincial governors, and even Caesar himself. In the NT it is similarly used as a 'wide' term, applying to procurators--Pilate, Festus, Felix--and to general 'rulers' (Mt 2.6). [The New Intl. Dict. of New Test. Theology (ed. Brown) gives as the range of meaning: "leader, commander, chief" (vol 1.270)...this term would have applied to Quirinius at MANY times in his political career, and as a general term, Syria would have had several individuals that could be properly so addressed at the same time. Remember, Justin Martyr called him 'procurator' in Apology 1:34, which is also covered by this term.] My point is...nothing is really out of order here...
http://www.christian-thinktank.com/quirinius.html