We already solved the birthday celebration problem. The Queen's official birthday in Canada is May 24th. Charles' official birthday in Canada will be May 24th. We just decided at some point the best monarch's birthday to celebrate is Queen Victoria and have stuck with it.

The Dutch continued celebrating Queen Juliana's birthday (April 30th) as their national day when Queen Beatrix succeeded her, as they didn't want to move an event which is traditionally celebrated outdoors to January.

Beatrix was succeeded by King Willem-Alexander, who was born on April 27th- so the national day moved to his actual birthday. April 30th is now known mainly for confused tourists expecting a party that happened three days earlier.

We don't really update it for each new monarch, it's just a set of rules. They were last changed fairly recently, to remove male primogeniture in case Prince William had a daughter as his first child (though he didn't). Every single Commonwealth country had to pass its own individual bill amending the Act of Succession, and it finished in 2015[1]. It's pretty unlikely they'll change again any time soon, the only thing that's still up for much debate is the requirement that the person sitting on the throne isn't Catholic.

It'd be a hell of a scandal if these laws got out of sync, and yet it would be one of the stupidest scandals in history.

[1] https://en.wikipedia.org/wiki/Perth_Agreement

Ah! Good ol' DNS. Nothing can go wrong now!