If you look at history and the records and do the math, then it comes out to 2 or 3 BC late September.
I agree with you,
From John the Baptist being 6 months older than Jesus, and his father serving in the 24 courses of Priests in the Temple, and from the 15th year of Tiberius being 28 AD, etc.,
I think Jesus was born very late September to very early October in 2 BC. Likely on the Feast of Tabernacles?
If this is true and if you understand the 70 weeks prophecy of Daniel Chapter 9 and the count of days from the restoration of Jerusalem (and the wall) being from March 14th, 445 BC to 483 years (173,880 days) exactly to April 6th 32 AD, with the following week (7 days) being the most important week in human history, then something interesting jumps out, I was actually surprised to discover this,
If he was born in that time-frame, he would have been 33 years old to the very day (11,880 days) within the crucifixion week,
March 14th, 445 BC ——————483 years| April 6th,32 AD
September 27, 2 BC -——————33 years| April 6th,32 AD
Something else jumps out also, I personally think of Christmas as nothing more than a repackaged Babylonian heathen festival, however if the above dates are correct, and with the normal gestation period of a human as 280 days (7 x 40 days) then he would have been conceived by the Holy Spirit on or about December 25th of 3 BC.