The (hand waving!) way I understand it, redshifts of z>0.1 are considered to be cosmological in nature and although there is no way to distinguish between (relativistic) doppler redshift and cosmological redshift for measurements up to around z=1.4 (which equates to an apparent recession speed of c), once you are looking at larger redshifts they cannot be due to relativistic doppler effect due to the limit of c on any differences in apparent velocity due to classical momentum and energy transfer.

Surely, once we are considering high redshifts and apparent superluminal recession speeds, where relative inertial motion is a negligible factor, the cosmological component of that redshift would be absolute? i.e. however fast you were travelling through space, you would observe that distant galaxy to be apparently receding from you at a speed faster than light.

If the expansion of the universe causes the wavelength of light to be "stretched" (by introducing extra space into the proton during its journey, for instance) then if that light had been travelling for billions of years it would be "stretched" by an absolute amount and any difference in the relative velocities of emitter and observer that are caused by their relative inertial movements would add or subtract only a small and apparent value to that absolute amount?