Your honor, I would like permission to treat watchwolf as a hostile witness, because I believe he is being disingenuous.
I can see that you will stop at nothing to learn the truth. First I have to tell you where to find the most famous story in the world, and now I have to spoon-feed you the verses so you can connect two dots.
Luke 1 (mea culpa, I should have told you that Joseph is also mentioned in chapter 1) introduces (v 26-7) Mary and Joseph as residents of Nazareth, and says that Joseph is of the House of David (and incidentally, Luke attempts to document this in chapter 3, giving a genealogy for which 2000 years of diligent scholarship has been unable to find a shred of verification, that differs with the other genealogy of Jesus from Matthew 1 in almost every name between Solomon and Joseph, and that most secular scholars think was invented).
Luke 2:39 makes it explicit that Nazareth is their home: “39 And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth.” If you read the preceding verses, you will see that Luke is talking about the period six weeks (the length of a woman’s “purification” after bearing a son) after Jesus was born, right after he was presented in the Temple. So Nazareth was clearly their home before Jesus was born, contradicting Matthew.
So why did Joseph have to go to Bethlehem? You gave up your tireless search for the truth just one verse early; you quoted Luke 2:3, but all you had to do was read Luke 2:4 – “And Joseph also went up from Galilee, out of the city of Nazareth, into Judaea, unto the city of David, which is called Bethlehem; (***because he was of the house and lineage of David)”
Emphasis mine.
Lest you think that I cherry-picked the now deprecated King James version because it is favorable to my case, here are a few dozen other translations of that verse, from almost every published Bible in English:

Luke 2:4 - Bible Gateway
Again, in case you forgot, David lived a full 1000 years before Joseph.
And just in case it needs to be explained, I’m not claiming that Augustus ordered this insanity, Luke is. I honestly don’t see how anyone could believe it. You said all this seems plausible because you have to file an out of state tax return. Tell me, suppose President Hillary tears up the constitution, as we all know she will, and gives the UN full authority over the US, and they require you to file your tax return in the city where your ancestors lived 1000 years ago. Would you have any idea where that is? I have the intertubes and the google machine and all that stuff, and I can’t trace either side of my family back past the 19th century.
Although I’m pretty sure I’m descended from Thor.