I don't think it's necessarily a density issue as much as a residual stress issue.
Since foam expands (even non-expanding foam expands a little) as it cures, and the outside hardens first, you end up with residual tension on the outer surfaces, and residual compression in the middle.
When you "skin off" the surface, you remove a tension field and the blade moves to find equilibrium again.
You get the same thing with steel, but since it contracts as it cools (both from delta-T and a nasty phase change) you get the opposite, tension in the middle and compression on the surface.
I don't know if there is an equivalent to annealing where foam is concerned. You might try warming a piece a little, not enough to melt it, but enough to make the outside "relax a little" and be more accommodating to what the foam in the center is trying to do.
It might be a fun experiment to place a piece in a large pot of boiling water. Once it is cooled, cut a little from on surface and see if the distortion is less pronounced.
I've also heard of using the exhaust from a car to gently heat up plastics. It might work with foam. Be careful if you try this.
Have Fun,
-Dan M