This has already happened, actually. Some leap seconds have been skipped iirc due to faster rotation from all the impounded water in reservoirs in northern regions.
We should draw tidal power until there are exactly 360 days in a year, to make the arithmetic nice, and incidentally give us 24 minutes extra sleep.
The other way of doing this is just pushing the earth a bit off its orbit. Better to do it in the other direction though to stop global warming. Let's make it 400 days instead.
360 is much nicer than 400 though. 12 months of 30 days each versus 10 40-day months or 16 25-day months.
Yes, 360 is a superior highly composite number, and we would move through the sky exactly 1° per day.
Better yet, slow down the earth to 25 hours so that we're 1-1 with Mars!