I don't understand, the same ±1 day variation we have each year will stay the same? Do you mean the day of month? These are already spread out (20th, 21st, 22nd, and 21st, ±2).

So instead of the summer solstice being 21 June ±1, it will be month 6, day 4 ± 1 every year. (Assuming the year starts on what is now 1 Jan. (Spring is month 3 day 23, fall month 9, day 13, winter month 13 day 1). Seasons are still 91.25 days, or ~13 weeks. That just now means 3 months one week instead of 3ish months.

The moon phase of 29.54 days won't align, but it doesn't now anyways. So instead of months with 2 moons, we'd get months with no moon. Might have to change "one in a blue moon" to "on a moonless occassion". And imagine the killer party when day 0 or day 00 aligns with a full moon!