I am still grappling with the idea that a longer wave would have a higher frequency than a shorter wave. This implies to me that the longer waves will propogate much faster. With just a single layer of constant density fluid of course we have no vertical shear of the horizontal velocity. So, you have the linearized pv equation in terms of the variable eta, which has one additional term compared with the rigid lid equation for psi. Note that a key property of Rossby waves is that they are dispersive .
Different wavelengths have different phase speeds.
Rossby waves, surprisingly, are everywhere. Perhaps we should call all these 'vorticity waves'. The beta effect is the Earth's curvature, and short waves don't 'feel' that curvature very much. Thus a short blip on the jet stream would indeed to move slowly relative to the mean flow, and a long-wave distortion to propagate faster. Rossby waves in the lee of mountains.