Re: How the hell does a star change its rotation?
Starquakes seem to be the generally accepted reason for 'Glitches', where the rotation rate of a neutron star suddenly increases, but cannot be the solution for sudden slow-downs in rotation rates, let alone reversals.
The starquakes are believed to occur in the outer non-degenerate matter crust of neutron stars due to long-term cooling [of the neutron stars]. As the degenerate neutronium core cools it contracts and this occasionally leaves microscopically small cavities between the thin outer crust of 'normal' non-degenerate matter sitting on top of the neutronium core. Eventually though, these cavities will collapse and, because of the intense gravitational forces, when they do collapse you have immense quantities of mass accelerating at of thousands of 'G', resulting in the starquakes.
Because this is the result of contraction, the result can only be a speed-up.
I think any apparent reversal of rotation of a neutron star must be due to observational error; even a slowly rotating neutron star will have an enormous amount of rotational inertia and it's difficult to imagine any scenario that could both nullify and then reverse that inertia, excepting perhaps, collision with another neutron star. But then if we can see the neutron star in the first place, before any reversal occurred, then we'd also see a collision, if it occurred, because it would be a highly energetic event.