The Jewish day is reckoned from sundown to sundown. Although I agree with everything else you wrote, I think we need to consider the differences in how a day is viewed in Israel.
Born after sundown(?) the first day of the Feast of Tabernacles (Bullinger dates it Sept 29, 4 BC) and the angels make the announcement to the shepherds later that same night? — “The Circumcision of our Lord took place therefore on the eighth day, the last day of the Feast, the “Great Day of the Feast” of John 7.37.” From Bullinger below.
Night would be from sunset to sunrise, and still the same day.
Night was divided into watches - according to Bullinger Appendix 51
New Testament.
First Watch, 6 p.m. to 9 p.m.
Second Watch, 9 p.m. to midnight.
Third Watch, midnight to 3 a.m.
Fourth Watch, 3 a.m. to 6 a.m.
Interesting topic that I had not so carefully considered.
Note in the link that Bullinger dates the “begetting” as 12/25 5 BC - Gives a true Biblical reason to celebrate the Word becoming flesh on December 25 and setting aside the pagan influences associated with this date.
DATES OF “THE BEGETTING” AND THE NATIVITY - Bullinger Companion Bible Appendix 179
https://levendwater.org/companion/append179.html#begetting
51. MONEY AND COINS, WEIGHTS AND MEASURES.
https://levendwater.org/companion/append51.html
Interesting.