To add to the discussion of when Jesus' conception and birth may have taken place, I offer this interesting essay about the division of  Abijah that Zechariah served in, and what can be gleaned about timing in Luke 1 from that service.
 
http://doig.net/NTC07.htm
 
If the essay noted above is correct, then did Zechariah serve in the Temple duing the Feast of the Tabernacles?  Did Luke, a Greek, write "month" thinking of the Hebrew calendar, and if so, which: the religious or civil?   Since Luke was Greek and addressed his gospel to Theophilus, who was possibly also a Greek, was Luke referring to their own calendar which at that time was probably the Syro-Macedonian?   Or, as EAR pointed out, is the sixth month that is mentioned the month following the fifth that was just previously mentioned in Luke 1:24?
 
I believe what it comes to is this: we won't know for sure this side of heaven!  We can and should study the Word, and it is edifying to understand the times in which it was written.  But truthfully, we can't be sure of the date, nor the season or year.  Likewise, not one of us can say with all authority that our theory is right and others are wrong.
 
It can be argued until the Lord returns, but this is what is known for sure: Jesus was born, the King of Kings and Lord of Lords, to save ourselves from our own sinful ways.  He was born so He could die to create a sure way for us to be redeemed.
 
I find it very interesting that we cannot know the day or hour He came the first time, even as we can't know for the next time.  Perhaps He wants it that way so we keep on keeping on with serving Him right up to the moment of either the Rapture or our mortal death.  While study is important and edifying, it isn't study for study's sake that we are called to do, but study so we can grow more like Him, being drawn into obedience to His Spirit.
 
This I know: He is coming again!  Praise the Lord!