Born or re-born or re-erected or whatever?

But like, their local tax season, right? From what I remember they had travelled to pay taxes, but the Romans didn't wait until April like America does.

Actually, did some quick searching and it looks like the Romans were forcing (I think Jewish people, but it may also have been regional? Sources are giving me different things and I can't be bothered to log into my account that gives me access to scholarly articles) people to register for a new tax. Since the Romans at the time would usually tax in cycles of like, 5-15 years, if they followed a structured system at all (It also seems like there wasn't income tax or taxes in individual assets, but they would tax transactions and import/exports mostly). But If I was going to set something like that up, I'd do the registration due near the end of the year. I think they were using the Julian Calendar whish largely lines up with the current day calendar, at least in the year end/beginning. Best guess from what I've seen is they likely were there during the Jewish holidays right after the fall harvest.

So it seems like they waited until after the harvest was done, then had to travel to get registered by end of year and got there and popped out baby jesus around Sept/Oct (ish).

Of course that's assuming any of those stories have any validity. Historical consensus is coming around to admitting how little evidence for a biblical Jesus there actually is. Since there are no contemporary writings and all of them were telling this story decades, if not centuries later, it's super easy to just line up your stories with the way things happened in the past.