If I were Pope Gregory’s advisor, I’d urge this: all months to have 30 days until the first (or last) of some month falls on a solstice or equinox; thereafter, alternate 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 30¼.
Unrelated link: Questioning 7/4
Or all months have 30 days, with one day inserted for every 68.67 normal days. (With the Julian approximation that would be 68 4/7 exactly.)