Yes, I think this sounds reasonable, although even when the bar magnet has stopped spinning, there will be a magnet traversing a terrestrial or interplanetary magnetic field so there should still be a change in the magnetic field and an induced current (although maybe not AC anymore, unless analyses over the complete orbital period).

The rotation of the magnet should definitely slow, as is the case with tumbling rocket bodies and satellites that have lost control. The interval of flashes from a light curve measured for a tumbling satellite slows over time until it is deemed constant, but I don't know if this is a limitation in the measurement technique or whether the object has in fact "stopped" tumbling. I would suspect secular variations, solar radiation pressure, etc to play a role and change the orbit, further complicating matters.

I was looking for some research that I have seen presented on the characterization of tumbling rocket bodies, specifically the effects of solar radiation pressure, but couldn't seem to find it. I was able to find another nice condensed summary with links to the theory and applications at the bottom of the page (http://www.satobs.org/tumble/tumbleintro.html).

I am not a cosmologist, but I believe you may find a related discussion pertaining to either Quasar or Pulsar Stars.

I hope this helps. Best regards!

I have some thoughts on this to share. I am not 100% sure that all I will say is correct. Here is just a hypothesis based on my knowledge and some relevant experience.

A rotating magnet will be a source of EM radiation around a frequency Fo that is defined by its angular velocity w=2piFo. If its size is about a half and above of the wavelength wl = 3e8/Fo then it would radiate efficiently EM energy. This leads to loosing its rotational kinetic energy and even mass (in a negligible quantity). The kinetic rotational energy is E = 0.5Iw^2; where I = k*mr^2 is moment of inertia,  r is radius and k depends on a body shape, e.g., 2/5 for a spherical object, 1/12 for a thin rod and so on.

Reduction of the kinetic energy transformed to the EM radiated energy would slowdown the spinning speed wand, thus, decrease the radiation frequency Fo while assuming the mass is not changed. Thus, the radiation spectrum will be "red" shifted gradually to lower frequencies. At some point in time, when the wavelength becomes large or too large compared to the body dimensions, the EM radiation mechanism becomes less efficient until it would be only the EM energy stored predominantly in the near field zone with a little or without transition to the radiation zone. At this moment and around, the energy loss through the EM radiation will be low. It seems like the system should even evolve to a steady state with a residual spinning velocity.

I believe something similar might happen in fast spinning neutron starts with already observed slow down that was not yet well explained. I am not an expert in this field but I read some popular articles about.

It would be interesting to play with a coupled system of mechanical and EM equations to predict dynamic of this funny physical process. It could be an "analytic" solution derived through a little programming in a computer algebra system.

I have considered a rotating magnet for VLF transmissions because it is likely to be far more efficient than an induction loop, which suffers from skin and proximity effects in the wire. This, of course, is not a radiating system because the frequency is far too low. If the magnet has a good shape factor then the magnetic moment of such a rotating transmitter can be shown to be proportional to the product of the volume of the magnet and its remanance.

It is interesting to consider how the effects of radiation and external resistance manifest themselves with a rotating magnet. The following discussion is somewhat heuristic, but it captures the essence of the problem. It is an edited version of what I wrote in my PhD thesis…

For a conventional magnetic dipole the field collapses and reform every half-cycle. If we consider the field lines to be restricted to moving at the speed of light, there is a limiting distance, at wavelength/4, where the field cannot not collapse and re-form fast enough. In broad terms, this means that the field lines become detached and "float away", to form the radiation field. A more precise analysis gives the characteristic distance between the near and far field (the transition distance) as as wavelength/2pi. The analogy for a rotating magnet is that we would expect a transition zone to occur at wavelength/2pi where the radial velocity would be c. For field points further away than this, the field cannot be dragged round fast enough by the rotating source so, in essence, the field lines break free and radiate.

The manifestation of this radiation field would be a force tending to oppose the rotation of the magnet and so it is analogous to the radiation resistance of a conventional transmitting antenna. Similarly any frictional force opposing the movement of the magnet is analogous to the ohmic resistance of a wire antenna.

It would be difficult, in a practical earth-bound system, to spin a magnet at more than, say, 60,000 rpm, corresponding to a frequency of 1000 Hz. At this frequency, the wavelength would be 100 km and the transition distance 16 km.

I concluded the discussion, in my PhD thesis by saying “Entertaining though this speculation is, the effects are, of course, so small as to be immeasurable” but that does not mean that an essentially non-radiating system using rotating magnets does not have its applications.