If we’re okay with having a leftover day (or two), let’s just have 5-6 intercalary days and then we can divide the other 360 days as evenly as we want. I’m a big fan of 12 months with 30 days each, with 3 weeks of 10 days each. But 360 is so versatile you could do it however you want.
Since the days of the week originally get their names from the sun, moon, and planets, we could easily name days for the 3 planets that have been [relatively] recently discovered or recognized: Earth, Uranus, and Neptune.

Basically I’m advocating for the same structure of the French revolutionary calendar, but I’d change it so that the year starts on the Gregorian calendar’s March 1 to line up the leap day, and also copy the Gregorian calendar’s leap year calculation.

Probably when my roommate tried to kill himself a few months ago.
My sister tried to hold his wound shut and led him outside.
I held the door shut to keep him from getting back to the knife, called the ambulance, and cleaned up all the blood the next day.

Still feels kinda surreal.