Man... they're going to need some serious computing power to figure that mess out!

I mean, how do you have lunar calendar, when you're on a completely different planet which has two moons?!

I suspect you're probably right, they'll switch to a time signal from Mecca or Jerusalem, because there is no other way to resolve the conflicts that I can see, not without it becoming utterly arbitrary.

But then.. you run into speed of light lag... Oy vey!