As already stated, the argument from silence is a logical fallacy.
We don't, at present, have the evidence to know whether Cyrenius was Legate in Syria at the time he fought against the Homonadesians in Galatia, 10 BCE - 2 BCE.
Therefore, you cannot claim that he wasn't governor in Syria.
Also, Augustus did pass a decree in 8 BCE requiring an empire wide census. It may have been this decree that led to the enrolment in Judea, carried out by Herod.
Without a doubt, the people living at the time, or even near the times, would have had a much clearer understanding of the history. And there is nothing written in Luke that is contradicted by Josephus.
Man, you use Josephus when it suit you, and then disagree with it when it don't.
From Antiquities of the Jews, Book XVII, chapters 1 to 3, we know that Gaius Sentius Saturninus was legatus of Syria from 9 to 7 or 6 BCE. And Publius Quinctilius Varus, from 7 or 6 to 4 BCE, Book XVII, chapters 5 to .
Varus was Saturninus' successor to the legate of Syria:
Antiquities of the Jews XVII:5:2 said:
2 Now, Quintilius Varus was at this time at Jerusalem, being sent to succeed Saturninus as president of Syria, and was come as an assessor to Herod, who had desired his advice in his present affairs...
The "affairs" being the intrigues that went on between him and his family, culminating with the execution of his son, Antipater in 4 BCE (XVII, chapter 7), just before Herod's own death (XVII, chapter 8).
Judaea was divided between Herod's children, with Archelaus getting Judea and ruled for 10 years before he was banished to Vienna (XVII, chapter 13), and Judaea became a new Roman province in 6 CE, Book XVIII, chapter 1.
Varus served long enough after Herod's death, to put down a revolt against Archelaus' rule, in 4 BCE, Book XVII, chapter 9.
In none of these chapters in book XVII (from chapter 1 to 12), do I find any mention of Quirnius or Cyrenius as legatus of Syria until at the end of chapter 13, or the census wasn't mention until Book XVIII, chapter 1.
More detail about Quirinius in Book XVIII, as well as Coponius, the newly appointed prefect of Judaea.
You keep forgetting about Saturninus and Varus, or simply ignoring these 2 governors who were around before Herod died.