Hapgood's initial idea was that the ice build up around the pole(s) would be sufficiently imbalanced (as e.g. it is now in Antarctica) that the centrifugal forces would cause the shifts to occur where a new polar ice build up would begin that would eventually cause another shift. Apparently this idea has been discredited. Considering that Einstein accepted this mechanism a possibility, I'm not sure how discredited it could be. But no matter. We don't really need to know the mechanism to believe that it occurs. It's amazing to me how many things that have absurd explanations in Geology texts (e.g. mountain formation) can be simply explained by the crust shifting over the oblate core.
ML/NJ
A little bit of spit or hair grease can affect the rotation of a baseball. So I guess billions of tons of ice added to or subtracted from could affect Earth’s rotation as well.
You know... There is another physical connection I very rarely see discussed that could also influence this. Center of mass Barycenter of the Earth/Moon lock, and the Barycenter lock of all planets and the sun in the solar system that do affect each other especially during particular alignment events. We are dancing a jig as it is, and this could also have great crustal influence.