I propose that we just extend "year day" to cover the entire year and leave only a single month called Null. This solves not only leap days but also leap second

I propose that we just extend "year day" to cover the entire year and leave only a single month called Null. This solves not only leap days but also leap seconds and even timezones: The time in year day isn't part of any month, day, hour, or minute so there's no problem.