Why do I think 'c' is 'c' in all motion? One good reason is that motion is weird

If you look at it classically motion is one thing, about displacements measured in time. But if you use relativity we get to several new conclusions. We have uniform motion, also described in relative motion, then we have constant uniform accelerations, and finally all other types of accelerations. Let's call it three types to start with.

But the first definition, uniform motion, also becomes a relative motion. Relative to what you measure against. And locally there is no proof of this first type of motion existing, you need to introduce frames of reference to prove it. That means that you need to pick something not locally to compare against, to get to a uniform motion. But we probably agree that as soon we have tree objects in different uniform motion we have a proof of different uniform motions existing. You can also use incoming lights blue and red shift, or the CBR, for defining the same.

But

You're at rest in any uniform motion, and being at rest is translatable to still. So now we got four types. Where two is about the same type of motion, uniform 'relative' motion.

If we want to define 'c' to a arrow, I think we can do it two ways. One is a very strict definition of locality in where we can assume instants of displacements as being 'still' in any acceleration, connecting those instants to the idea of 'constants', and 'one frame of reference'. The other is different, and not as satisfying to me. In that one we also will use 'locality' but now define it as this local focal point 'frame of reference' can be transformed by motion, mass, energy etc. That means that this frame of reference still exist, but also should be locally adaptable to the relations around it, 'adapting' in some weird way. What talks against this one is the fact that you can introduce a accelerating rocket together with three uniformly moving objects, being at different uniform velocities. Each one of the uniformly moving will define different time dilations, and Lorentz contractions to the one accelerating.

You don't need a twin experiment, you just need to decide if you believe in different clocks measure over frames of reference, or not. And the choice isn't even there, NIST has already proven that one, conclusively here on Earth at decimeters.