Let's start to answer your point of views.
i just answer some of the questions here, and if im OT well many of us here are OFF TOPIC.
it is clear to my opinion that my answer is: No
Jesus was born on this event of Caesar Augustus ordered a registration of all citizen in their Birthplace (Luke 2:1-3). It will be easy for them to collect tax in this decree. it will be unwise for Augustus to order a decree which will be very difficult for the people to travel if it is in the month of December. and it will be much harder for Mary and Joseph to take this journey on winter since Mary is due Pregnancy, 90miles from Nazareth to Bethlehem. Also after they arrive and give birth to Jesus, in the Bible account says that a group of shepherd are out in the night watching their flocks. (Luke 2:4-

which it will also be hard to believe if it is in December since it is winter in Bethlehem and No Shepherd will go out feed and watch their flocks at night!
about the "first century people..." you've mentions, that is absolutely incorrect, kindly read this for your referrence (
Ancient Roman Holidays & Festivals at The Detective & the Toga)
lastly on your last quote: there is no 0 in between B.C.E and C.E. (or A.D.)
Jesus was born in the middle of 6 B.C.E to 2 C.E (A.D.)
"dili diay mo close kay once a year or twice ra man... close kami kay everyday bonding!"
