ok, to clear this up:
First, I believe that my method to synchronize stationary clocks is at least some achievement (I don't think anyone thought of it before, so I called it "wespe method"). However, I had also assumed that my method could be used to synchronize moving clocks, because I thought all relativity effects would be nullified by the setup. If I was correct, relativity of simultaneity would have to be wrong, and relativity would collapse.
Although I can't work out the exact math, I still think relativity effects are indeed nullified. If we analyze from the moving astronaut's frame: 1-Length contraction: this scales the distances equally in both directions, average would be same. 2-Time dilation: this causes both clocks to run slower equally, same here. 3-Relativity of Simultaneity:This causes a shift in both clock values, same (remember my setup already had an offset). So I don't think any of these will change the average for the moving astronaut.
Only problem I found is the doppler effect (non relativistic doppler, since I considered time dilation separately). So, what I failed to provide, is a formula, instead of (a+b)/2, that would not depend on distance to each clock, while the doppler is in effect. Failing that, I withdraw my argument.
Thank you.