Lewm
There is effectively no damping effect available from the two opposed magnets. Eddy currents are proportional to field strength times relative velocity divided by electrical resistivity. The configuration used results in low relative velocity. The electrical conductivity of available magnetic materials is quite high - NdFeB magnets have about 100 times the resistivity of copper.
For all: A distinction needs to be made between velocity dependent drag, which will tend to stabilise the system against speed variation and classical friction (velocity independent) which will not. Hydrodynamic drag and eddy current effects are in the former camp, standard bearing friction and stylus drag are in the latter.
Mark Kelly