You have correctly correlated reverse rotation and ice ages. They also know: [link to www.livescience.com
Ice ages have something to do with earth's tilt. Why?
If earth is charged and spinning (think of it as a current loop), we can force it to spin in the opposite direction like this: [link to www.youtube.com
The important point to notice, is that by Lenz's law, we can change the direction of the current by changing the INTENSITY of the magnetic field. We do not have to change the DIRECTION of the background magnetic field.
So how do you get changes in magnetic field strength? Assume that our solar system is spiraling along in a Birkeland currrent, in a background field. Then get rid of one oversimplification that we usually make: We usually assume that the source of the background field is very distant. If it is not, then our solar system spirals in towards increasing field strength, and out. We therefore have a mechanism where earth's spin direction is dependent on where earth is in it's Birkeland current spiral
. We have already shown that precession is caused by our solar system spiraling along a Birkeland current, with the axis of our solar system aligning with the filament. So we are left with the correct relationship: Earth's spin is driven up or down (even reversed) depending on where we are in our precessional cycle.