special relativity - How can time dilation be symmetrical?

I recently posted a version of the twin paradox with a twist but here I'd like to propose a new thought experiment all together. Take two clocks, A & B, and place A 1 AU away from B. Once the clocks are separated and stationary relative to each other sync them up again; to do so send a light pulse from A to B, and when the pulse reaches B the clock will start ticking while A waits the exact amount of time it takes light to reach B to start ticking. The idea is to have two clocks that are in sync but separated by a large distance, and I imagine there are multiple ways to do this. Now take a third clock, clock C, which is also synced with A and B and have it travel the distance between A and B at .866c so that time runs at 1/2 the rate for clock C. However to Clock C, A & B would be running at half speed. When it arrived at B though we'd be able to compare the elapsed times and say for sure whether C or A & B had in fact been running slower, even though special relativity dictates both viewed each other as running slower and both are correct. The only decent explanation I can think of is that for C, simultaneity between A & B is broken rendering B's readings inaccurate, but that still leaves us in a very bizarre place as ultimately to C, B should read half the time and to B, C should read half the time.

*Note: Please don't try and use acceleration to explain the disparity, it is a common misconception that acceleration resolves the twin paradox when its actually that acceleration is used to confirm the change in reference frames. To avoid that conundrum all together you can imagine that clock C was already up to speed when it passed A and synced itself up with A as it passed C. Furthermore we can imagine C never actually slowed down when it passed B, rather it just took the reading from B to compare. This way C is in one inertial frame for the entire duration of the experiment.