Pentcho,
I already tried to clarify that your mistake in this case has not yet anything to do with Einstein's "conventional" relativity. Relativity is a principle that nobody will seriously question. What Einstein called his postulate of relativity is something quite different, and I consider it as putatively natural as misleading.
Einstein's relativity demands to change the still valid most basic notions time and space for the sake of Lorentz covariance.
My argument against your reasoning is based on the valid notions time and space as well as on the Galilean principle of relativity and on the also proven Doppler effect. Again, I do not refer to Einstein's "relativity".
Let's look at your statement "when the observer starts moving away from the light source, the frequency he measures decreases but the speed of the pulses relative to him remains unchanged."
Well, the observer receives a signal with a smaller than original frequency if his distance from emitter steadily grows than in case it remains constant. This is known as Doppler effect. However, why the heck do you attribute a "speed of the pulses relative to him"? I can you tell why. You tacitly changed your perspective. In that you are in company with Him:
As Stachel wrote in the paper you repetitiously quoted:"Einstein's version of the relativity principle (minus the ether) requires that, if this is true for one inertial frame, it must be true for all inertial frames. But this seems to be nonsense."
If we are using the good old notions time and space as I did for my lifetime this is indeed nonsensical, as nonsensical as your change of perspective.
Eckard
