As indicated above, the steering damper is unlikely to be the primary fault. By far the most common problem is swivel preload - and your check will not have determined whether they are at fault or not. To do this, the track rod and drag link need to be disconnected and the resistance to movement checked. Only gross free play will have shown up with the check you made. The other likely candidate is the bushes on the ends of the panhard rod.
But you also have to be aware that there may not be a single fault - the wobble may result from the accumulation of several small problems - fixing one may stop it; until the others get a bit worse and the wobble returns.
John
