I have considered numerous variations of it, but all these variations had 30 days in the leap month (Nu).
I recently considered the possibility of having 29 days in the leap month (Nu). This would produce years of 354, 355, 383 & 384 days.
Then the new year rule needs modifying slightly to keep it workable and I change it to
"New Year's Day must always fall in the first 29 days of the month of Alpha."
Then many more years must have an extra day added to the month of Zeta and a rough calculation to 4 decimal places revealed that 9/16 years would need an extra day added to Zeta. Then the calendar has a 11,600-year cycle just like my Annuary calendar
This is not the only similarity to my Annuary calendar. If the leap year rule of the Gregorian calendar were modified, the mean month would be the same as it would be if the Annuary calendar rule determining the 29-day intercalary year were modifies to produce exactly the same mean year.
The 16-year cycle for a 29-day leap month is much shorter than can be obtained from a 30-day leap month for a calendar of similar accuracy.