How are the Gospel accounts of the ritual of marriage of St. Joseph and Blessed Virgin Mary reconciled?

Luke 2:5 gives an account of Joseph who went to Bethlehem for enrolling in the census with Mary who was pledged to him in marriage. Matt 1:18-25 however, states that Joseph took Mary home as his wife on the instructions of the Angel, after 'finding her with child.' . If the journey to Bethlehem did not take months, Mary would have been well into the advanced stage of pregnancy when they commenced the journey. How come that they were still at betrothal stage when they started for Bethlehem? Is it possible that they completed the final ritual of marriage after reaching Joseph's hometown? But then, how does it match with the account of Matthew? My question therefore is : **How are the accounts of completion of the ritual of marriage of Joseph and Mary reconciled in the narrations of Matthew and Luke?** Views of scholars of any denominations are welcome.