What exactly would be so troublesome with having a “special day” outside of the usual week/month cycle? You can still go worship on whatever day of the week applicable to your faith. Just make the last day of the year its own thing. We can call it “New Years Eve” and party together.
It makes the calendar less than compatible with the commandment to keep the Sabbath by not working on every seventh day.
Which is not insurmountable in practice (e.g. by keeping a separate ecumenical calendar) but you can bet it would be a significant source of opposition.
But you’d be resting on the extra day, too (if you want, I for one will be partying). So you’d never go more than seven days without rest.
If that still doesn’t fly, I suggest we combine the extra day and the previous day into a mega-day that is 48 hrs long. Then everyone except programmers will be happy (we’re never happy with datetime conventions anyway, so what’s one more if-else statement between friends).
