Me:
So we can only conclude that the tradition about the day of atonement is just wrong.
That statement was intentionally glib because I didn’t feel like going down this particular rabbit hole that is ultimately based on unverifiable traditions and cannott be relied upon as historical.
But… if it is assumed that the story about Zechariah were on the day of atonement in the 8th course in 6 BCE (24 October), then the priest courses would actually match up for the first course on 30 August 70 CE. With a subsequent period of at least 15 months for Elizabeth’s 6 months and Mary’s pregnancy, that would place Jesus’ birth in… 4 BCE. (That would be a few months before Jesus’ presumed birth possibly around October; however it is also only tradition that Mary immediately became pregnant when visited by the ‘angel’, which is not stated in the story.)
Of course, it can’t be stressed enough that we don’t really know the actual circumstances of Jesus’ birth or death (beyond that he was probably executed), all of which is only in stories written many years later.