"1.It is a mathematical error to assume there is a rest frame.
2.There is no mathematical problem assuming a rest frame, but experimentally this rest frame never appears.
3.Under the mathematical description used by SR, which interprets experimental results, the term 'rest frame' has no meaning."
Nice thinking W (with the very long name that I now shorten to W)
You are right in that it is a arbitrarily made definition in Relativity, as long as we're not discussing local 'accelerations' in where you always will be able to define 'who did what'. But it has a, very local, meaning. Just as you are free to define the 'uniform motion' to you, you can, in part, or for the whole define it to your 'counterpart' when measuring.
And to measure a 'time' you need the 'local clock'. As that is the 'clock' you tick by, for real, or at least as 'real' as we can get it. You could ignore your own arrow of time of course, instead measuring by using other 'frames of references' clocks, but that would become a conceptual exercise, leaving yours undefined as long as you don't know all gravitational settings and the 'relative motion' of all involved.
As for relative motion it has no relevance to what you measure lights speed as. You can take how much 'time' you like to get from A to B and your local measurement using your local clock will always give you 'c' as far as I see.
In Relativity an acceleration is equivalent to 'gravity', and just as with the NIST experiments we know that different 'gravity' will deliver different 'clock rates' relative the observer studying those clocks. That's also the reason why in a two way experiment you can get different values for lights speed in a vacuum, as you will have a constantly varying 'gravity' in any (non-uniform) acceleration, as well as different time rates, depending on the clocks 'elevation' inside the spaceship, just as Earthside relative a clock in the atmosphere.
You can assume a uniform constant acceleration of course, at one gravity for example. But then you still will have that 'elevation', giving different clock rates, to consider when measuring the speed of light. Find a way to make a 'one way' measuring of lights speed in a vacuum and that problem should disappear, as I think of it :)
Or maybe not ::))
I really need to think about this one.