I don't know what harrowing is Dans, but a scarifier is like a big wire brush which scratches the moss out without damaging the grass (much). Ours is fitted into a cylinder mower which works really well but clogs quickly, so quite time consuming, although not compared to a lawn rake! We had far more moss than grass but, as previously said, the grass recovered completely. That may have been due to the weather as we scarified late Spring and the Summer heat finished the job.
I have seen seeding done after aeration- a cylinder which pushes holes into the ground. Grass seed is mixed with washed sand and brushed into the holes.