An accelerating clock is absolutely moving.
Yeah, what he said.
In relativity, the concept of "absolute motion" doesn't exist, so it is meaningless to say that something is "absolutely moving".
That statement is not exactly incorrect, but it is unclear enough to be interpreted in several different ways, some of which are incorrect.
Proper acceleration is absolute (in the sense that that the word is being used in this thread), coordinate acceleration is not, and there exists no inertial frame in which an object undergoing proper acceleration can be more than momentarily at rest.
I'm swinging a rock around on a string, so either the whole universe is spinning, or my rock is moving.
Yes. And according to GR, both viewpoints are valid.
At any given instant, it may be taken to be moving or not as one pleases. There is no inertial frame in which it is continuously at rest. But that's not the same thing as saying that it is always moving.
About the OP, I got a shortcut answer.
Let's get practical! The speed of light one way is impossible to measure, and the OP assumes that it is. In real life, we will never have to solve that kind of problem, because we will never face it, so it is no use to study it.
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