OK, still trying to come to terms with this, and these paragraphs in the wikipedia entry stuck out to me:
When a magnet with a symmetrical field is rotated about its axis of symmetry (as it may or may not do in a homopolar machine), people often ask whether the field lines rotate with the magnet. Field lines can be a useful visualization-aid in predicting the behaviour of some electro-mechanical machines, but are misleading in the case of homopolar machines. There are no field lines mentioned in special relativity or Maxwell's equations or the Lorentz force equation.
A magnetic field merely has a magnitude and direction at every point in space, and is only defined relative to an inertial frame of reference (i.e. a non-accelerating, non-rotating frame of reference). No one has ever succeeded in making a device that can tell whether or not a symmetrical non-conducting magnet, hidden inside a black box, is rotating about its axis of symmetry.
However the Lorentz force law predicts that a rotating conductive magnet should be detectable, at least in principle, by the electric field produced when its free charges separate radially due to the (absolute) rotation of the conductor within its own magnetic field. This is the basis of one construction of a homopolar generator. The failure to appreciate this difference between conducting and non-conducting magnets is yet another source of confusion.
So, it seems the question I am about to ask may be hard or impossible to answer, but I am going to ask it anyway: If the passage of electrons through the field creates a radial force on the magnet, is there not an equal and opposite force created on the magnetic field? Would that field be pushed away, and thus rotate in the opposite direction to the magnet, or do we expect the field to be 'locked' in place (like the Earth is 'locked' in place when we jump up).