If your records and observational skills are good enough, you could ignore the moon altogether and base your calendar on the sun, replacing the period between phases of the moon with the period between equinoxes. But this also generates problems, as the average length of a year is 365.2422 days, meaning even if you add a leap day every four years, over the centuries your calendar will still go out of sync. Whatever method you pick, you’re going to have to periodically add extra days to pad out the difference.
