May as well embrace the weird, cuz we dont orbit in exactly 365 days anyway. So theres gonna be leap year type adjustments anyway.
1 odd day from 13x28 is the perfect excuse for a new holiday too. And avoids having to figure out is it a weekday or not. It gets to be neither, a unique special holiday not tied to religion, nationality, culture, politics, etc (though many oppose it for reasons within those topics).
speaking of leap days, I also considered using a quad-year as a unit, integrating the leap day as a standard day. 365.25x4=1461. But that only divides by 3 and 481, even worse!