This NASA page says:

> The greater Earth’s axial tilt angle, the more extreme our seasons are, as each hemisphere receives more solar radiation during its summer, when the hemisphere is tilted toward the Sun, and less during winter, when it is tilted away.

It has this to say about the 26k year cycle you're referring to:

> Axial precession makes seasonal contrasts more extreme in one hemisphere and less extreme in the other. Currently perihelion occurs during winter in the Northern Hemisphere and in summer in the Southern Hemisphere. This makes Southern Hemisphere summers hotter and moderates Northern Hemisphere seasonal variations

So I guess I still have the same question, but complicated by the fact that models would have to account for a different effect in different hemispheres.