[gus_massa]

It's an interesting question. I must take that General Relativity course some day. Meanwhile, I have to guess ...

I guess you are correct and with small amplitudes the apparent speed is equal to the speed of light. For big amplitudes, I'm not sure.

[raattgift]

Pp-wave spacetimes (pp = plane-fronted and parallel) can with suitable separations can have arbitrary constant wave amplitudes. Such spacetimes admit a Killing vector field letting us have a sensible way of measuring the propagation speed of the wave. At any point where it is measured, the propagation is lightlike.

Parts of a spacetime around an equal-mass circular-orbit binary will be reasonably approximated by a pp-wave spacetime (edge-on, not too close to the sources, and over a duration where their orbit is negligibly contracting).