The induced magnetic field of the shell is like an extension of the internal solenoid, i.e. they both have the same pole orientation. Because opposite poles attract and like poles repel, the shell will be repelled from the solenoid. If the current running through the solenoid were to increase, the repulsive force on the shell would increase.
This is very easy to test. I have asked around and gotten contradictory answers on how concentric ball magnets would behave, roughly 50% say the interior surface of either pole on a hollow sphere has opposite polarity, which would falsify this model, and another 50% say the inner magnet would prefer an orientation like this model suggests.
The overall design is, conveniently, very similar to a two-pole brushed DC motor, a type of machine that has been around since two centuries, and so has a strong foundation. This motor below has a stator that approximates a ring magnet, and it can probably be assumed that a spherical magnet will behave similarly.
// edit: that comparison was based on false association, the stator motor magnets are radially magnetized
I am not entirely sure that the fundamentals are correct but I think they might be. Will ask around and test best I can whether this is how magnets would behave, if it is, it could be a valid theory for what causes the Earth to increase in radius, and also why the mass of the Earth is accumulated in a shell.