Why can't we rule out other synchronization procedures?

According to what I've read, it is generally regarded that Einstein's choice to have the speed of light equal in every direction is only a convention, and since there is no way to measure the one-way speed of light, any convention that has the two-way speed of light equal to $$c$$ is valid. But why can't we measure the consequences of this effect?

When we see a star that is 1 million lightyears away, we assume that the star is 1 million years old by the time we see it because we divide the distance by $$c$$. But what if the speed of light was such that it was $$10c$$ when moving towards us and $$\frac{10}{19}c$$ (I think I did that right) moving away from us, then shouldn't the star only be 100,000 years old? It seems like there are measurable effects to choosing an anisotropic speed of light. What prevents this measurement if we can estimate the star's age by other means?

• Can I get a source? I can see how to construct anisotropic light speed, but I need to see how math turns out in this case to answer. Because I suspect selecting not even values for $c$ would change how coordinates add up to $ds^2$. – acarturk May 16 at 21:28