Precession, as you imply has no effect on the climate, but changes in the
tilt of the axis certainly do. This has a period of about 41000 years. The
variation is not large, 21.8 to 24.2 degrees, roughly, and it seems that low
values are more associated with ice ages owing to the relatively low insolation
in summer in high latitudes.
The eccentricity of the earth's orbit is also quite a factor, and can be
much higher than the present value of 0.0167. Its effect depends on the
position of the perihelion with respect to the equinoxes. I'm not certain that
even now, despite advances in celestial mechanics, either the eccentricity or
tilt are known accurately back to 70 million years ago.

Tudor Hughes, Warlingham, Surrey.