That's a shame, it'd be nice to have a formula that "wrapped around" properly.
I've been happy with the rhyme for a while. I can't remember it properly (in my head it ends "all the rest have strawberry jam, except my grandmother who rides a bicycle"), but it's obviously enough.
Now that I see it all laid out, though, I wonder if I can do better -- "Odd is 31 days to July, then it flips." Now the people in school counting on their knuckles all makes sense.
I tried it well before you wrote your comment because I hoped that the alternating pattern would yield something short but February messes everything up.