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

Personally I am content to live with the cognitive dissonance produced by the OP question about the two accounts. However, with some mental gymnastics there may be a way to reconcile them.

In Luke, they travel to Bethlehem from Nazareth while they are still betrothed. She gives birth at an inn, and there is no mention of a being taken in to Joseph's home.

Joseph too went up from Galilee from the town of Nazareth to Judea, to the city of David that is called Bethlehem, because he was of the house and family of David, 5 to be enrolled with Mary, his betrothed, who was with child. 6 While they were there, the time came for her to have her child, 7 and she gave birth to her firstborn son. She wrapped him in swaddling clothes and laid him in a manger, because there was no room for them in the inn. (Lk. 2)

In Matthew, Joseph takes Mary into his home after his dream where the angel instructs him to marry her. 'Taking her into his home' is another way of saying they consummated the marriage, which took place in a legal sense at their betrothal. Normally their would be a procession and a feast before the bedding, but apparently not in this case. This fits with the report that. "He had no relations with her until she bore a son." (1:25)

“Joseph, son of David, do not be afraid to take Mary your wife into your home. For it is through the holy Spirit that this child has been conceived in her.,, 24 When Joseph awoke, he did as the angel of the Lord had commanded him and took his wife into his home. (Mt. 1)

There is no mention of where this takes place or of a journey to Bethlehem, so we may presume that the entire story happens in Bethlehem, perhaps at the inn mentioned by Luke, just prior to Jesus' birth. The next chapter describes the birth, from which we naturally infer that he took her into his home prior to the birth, but this is not explicitly stated. Matthew may have combined two sources - one about the annunciation, another about the birth - in a way that confuses readers.

To reconcile the two accounts of their marriage, one might presume that Joseph had relatives in Nazareth, and that he took his wife and son to that home after the nativity. The problem remains, however, as to why he would stay in an inn in Luke. This may be answered by the late hour of their arrival or by his family's home being overcrowded because of the census. Another problem is that it would also seem that if Luke's chronology is correct, the couple, although betrothed, was not 'married' at the time of the birth. This might be shocking to us moderns, but in ancient Judaism a betrothal was a legal marriage, so the birth would still be legitimate.

Summary: one way to reconcile the two accounts is to presume that Matthew's annunciation takes place at the inn in Bethlehem. After the birth, Joseph takes Mary into his ancestral home [perhaps the "house" of Mt. 2:11], where both the marriage and the birth were celebrated. Although the birth would then take place before he 'took her into his home,' the child would still be considered legitimate since they were legally married/betrothed at the time.

Both Luke and Matthew could be proved right in referring to Mary as the betrothed one of Joseph. One could construct a chronological order of events with the help of Gregorian calendar months, as follows:
April : The Annunciation. Mary can't wait to facilitate Elizabeth. She immediately departs for Zakaria' s place.
July : Mary comes back. Joseph visits her to tell about the Augustus Caesar order. Both of them would have to go to Judea to register- Joseph as David' s descendant and Mary as his betrothed wife. Mary discloses her pregnancy to Joseph and is worried about the long journey of four days. Joseph suggests they immediately start. Meanwhile, he receives instructions from the Angel. Joseph says they will solemnise their marriage in David' s town, among his relatives.
August: Joseph finds a place to stay somewhere during the journey and solemnizes the marriage. But he has to meet the census deadline.
December: Joseph proceeds to Bethlehem with Mary who is nine months pregnant. The inn keepers are charging hefty fees from non-residents coming in huge numbers. It is Business over charity, and they refuse space for the couple .Joseph takes Mary to the cattle- shed after losing hope of finding a place to stay.
So, Joseph and Mary solemnised their marriage on their way to Bethlehem for the census.

I think that this long question boils down to: "Why does Luke refer to Mary as a fiancée and Matthew as a wife?".

The word that both Luke and Matthew use is G1135 - gynē, which has two common meanings:

• 1. a woman of any age, whether a virgin, or married, or a widow
• 2. a wife

The same word is translated as "woman" in Matthew 9:20, 13:33, and 27:55.

The only difference between the accounts is that Luke includes the adjective "espoused" and Matthew doesn't.

Notice that in Matthew 1:20, the same word, also without "espoused" is also translated as "Mary thy wife", even though this was very early on, when Joseph first found out about her condition, before the angel had even talked to Joseph.

I think the choice of "fiancée" or "wife" or "woman" is simply a matter of the writing style of the authors and the translators, without any other significance.

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

We have very little information on the subject of the marriage of St. Joseph and the Blessed Virgin Mary.

In Bible times, Jewish marriage customs regarding a couple’s engagement were far different and much more stringent than those we are familiar with today, especially in the West. Marriages were arranged by the parents of the bride and groom and often without even consulting the couple to be married. A contract was prepared in which the groom’s parents paid a bride price. Such a contract was immediately deemed binding, with the couple considered married even though the actual ceremony and consummation of the marriage would not occur for as long as a year afterwards. The time between was a sort of testing of fidelity with the couple having little, if any, contact with each other.

It was during this betrothal period that the angel Gabriel visited Mary and told her of her impending pregnancy. It’s no small wonder that Mary was so inquisitive of the angel; she was still a virgin and would know no man sexually for several months, maybe as long as a year or more (Matthew 1:18; Luke 1:34).

Joseph soon became aware of Mary’s pregnancy, and this no doubt was cause for consternation on his part: “Because Joseph her husband was a righteous man and did not want to expose her to public disgrace, he had in mind to divorce her quietly” (Matthew 1:19). Jewish custom allowed that they be considered as husband and wife, though the marriage had not yet been consummated. The point is being made that Joseph and Mary had experienced no sexual contact with each other, as verse 18 “before they came together” points out. So, Joseph was in a quandary. Jewish law provided that his betrothed, because of her unfaithfulness, could be placed before the elders for judgment and stoned to death. But he was thinking to just put her away quietly without public knowledge. Betrothals or marriage engagements in those ancient times were binding and could only be terminated by an official divorce decree.

It was then that the angel appeared to Joseph in a dream (Matthew 1:20-25) and explained to him that all this was bringing about the fulfillment of prophecy that a virgin would bear a child who was to be the Savior (Isaiah 7:14), and “he [Joseph] did what the angel of the Lord had commanded him and took Mary home as his wife. But he had no union with her until she gave birth to a son. And he gave him the name Jesus.”

Luke 2:1-7 also confirms the idea that Joseph and Mary, though betrothed, were considered as husband and wife by Jewish customs even though the actual marriage ceremony had not been fully effectuated. So, Joseph and Mary were actually legally married before the birth of Jesus...

When were Joseph and Mary considered married?

Again there is very little information on this subject matter, but there are some pious traditions about it.

The Marriage of the Virgin is the subject in Christian art depicting the marriage of the Virgin Mary and Saint Joseph. The wedding ceremony is not mentioned in the canonical Gospels but is covered in several apocryphal sources and in later redactions, notably the 14th-century compilation the Golden Legend. Unlike many other scenes in Life of the Virgin cycles (like the Nativity of Mary and Presentation of Mary), it is not a feast in the church calendar, though it sometimes has been in the past.

The feast for the Espousals of the Blessed Virgin Mary, now only celebrated by some parts of the Catholic Church, is on January 23.

Marriage of the Virgin

The Feast of the Espousals of the Blessed Virgin Mary or Marriage of the Virgin Mary is a Catholic feast which is celebrated by certain parts of the Roman Catholic Church on January 23.

Luca Signorelli, The Marriage of the Virgin, c. 1490–1491, a predella scene for his Adoration of the Magi, with the discarded rods at left.