Dear Marts Liena,
Thank you for a well written, well reasoned, informative essay. I agree with most of your observations/opinions and was unfamiliar with a number of recent papers and experiments that you referenced.
You are clearly correct that Einstein, considered to have abolished ether with special relativity, restored the concept, in varying ways, but essentially viewing "fields as physical states of space", and more specifically "there is no space absent field".
I have for several years considered ether as that which light propagates through. I fully agree with Einstein that
"Space without ether is unthinkable; for in such space there would not only be no propagation of light..."
I hope you will read and comment on my essay which is related to yours:
Deciding on the nature of time and space
In your response to Otis, above, on the Michelson-Gale experiments you say:
"The biggest sticking point with respect to special relativity is that rotating frames of reference are used in this class of experiment, not the inertial frames required by Einstein's 1905 theory."
That is an extremely important point. I am becoming convinced that 'ontology is all.' Einstein clearly formulated a 4D-ontology based on inertial frames. It is not at all clear that rotation and gravitation fit in 4D, despite that special relativity is freely extended into these non-inertial frames whenever it is deemed necessary.
Anyway, I fully agree with you about the issue of ether "it definitely is not undecidable!"
Thanks again for your essay and good luck.
Edwin Eugene Klingman