This is surprising. I had always assumed that the length-of-day function is essentially a sine wave everywhere on the planet, and that the derivative would thus

This is surprising. I had always assumed that the length-of-day function is essentially a sine wave everywhere on the planet, and that the derivative would thus be another sine wave shifted by 90 degrees. When the day length is maximal/minimal (solstice), the day length change rate is near zero, and vice versa. That's still true in the more accurate model, even though the shape of the functions is more distorted.