Probably August as it would be some what ridiculous to do a census and tax at winter's start. Augustus would have hit them when they had more cash on hand, after the first harvests. Yes the RCC's propensity to incorporate and co-opt elements from other religions, they would logically not want to overthrow one of the most beloved holidays of the pagan world. Around solstice would work.

re two births: Wasn't it Jesus who said "Ye must be born again."?!!