So? I don't care if it's hot in December or not and presumably we can figure out a more sciency way to time crop planting. Not like the almanac is worth fuckall in a changing climate anyhow.
Make New Years Day it's own thing, not counted in a month (or just make the new 13th month 29 days long), and continue tacking on leap days to the end of February using the currently established rules.
The length of the year doesn't change and no seasonal regression. It has so many fewer exceptions than our current system that you'd wonder how we ever ended up with a 12 month calendar.
Yes and no. The days would be outside of the normal week (so they would be in a kind of an 8 day week), and they would be holidays to not mess up work schedules in relation to the fixed calendar.
Many facilities are 24/7 operations that can't just close for a holiday (ex: hospitals, first responders). It definitely would mess up people's work schedules.