Yes, Quirinius was again appointed governor of Syria in 6 AD til 12 AD, after Archelaus, son of Herod the Great, was banished from rulership. But it seems the census in which Joseph & Mary had to go to Bethlehem & register, was first ordered by Augie in 8 BC.(He also had them taken in 28 BC & 14 AD, not long before his death.) Quirinius was governor only during the 8 BC one, and, given the time it took for the word to be spread, it was likely 7 BC when J&M arrived at Bethlehem.
The magi told Herod they'd seen His star 2 years earlier, & it'd taken them that long to make it all the way to Bethlehem. Thus, Herod ordered the murders of all Jewish males age 2 or younger. He died soon after, in 4 BC. And God told J&M to stay in Egypt til Herod's son, Archelaus was no longer ruler in his father's place. That happened in 6 AD.
We cannot be exactly sure of the time of the Persian decree allowing the Jews to return to Judea. There are umpteen accounts of the timing.
The main clue for a later date of Jesus' ministry is John The Baptist beginning his ministry in 28 AD.
More Scriptural & historical evidence points to an earthly lifetime of Jesus being 6 BC to 27 AD. But, no matter exactly when it was, the MOST-IMPORTANT thing is, IT HAPPENED !
You are contradicting with Luke 3:1
Baptist John started to preach in the 15th year of Tiberius reign.
Tiberius became the Emperor from August 19, 14AD since Augustus died on that day.
15th year of Tiberius was from August 19, 28AD.
Jesus may have been baptized in the Fall of 28AD
First Passover was April 29AD
Second Passover April, 30AD
Third Passover April, 31
Fourth Passover April 10 or 11, 32AD when Lord died on the Cross.
27AD is way too early
Eliyahu