I really like the 11 month calendar better than the 10 month calendar. Yes it's a prime number but each month will have exactly the same amount of days (24) and days will always land on the same weekday. If we multiply the number of months by the number of days per month (11 x 24) we get 264 which is just one short from the number of days per year. To solve this, we'll add an extra day at the end of the year and call it Year Day. It is not a weekday and there for would be counted as a holiday. Remember, every multiple of four years, there is also an extra day. So, this would be called Leap Day and would come before Year Day at the end of the year. This would also not be counted as a weekday and you'd have a two day holiday instead. I also added equinoxes to the calendar. They are different times if it's a normal or leap year. This is the best I could do.

I made a calendar on Google Sheets. Click the link below.

https://docs.google.com/spreadsheets/d/1Eb7eXLXDgB_aLM99-uTZaldvo4S-QCUE6AG0EWNHa7w/edit?usp=sharing