You continue to make the false assumption that simultaneous measurements in one frame correspond to simultaneous measurements in all other frames. Observer O sees a light beam reach point R at time t, and records the arrival of O' at -vd/c also at time t. According to frame O', these events and associated measurements occur at different times. Your analysis simply doesn't work, because if you want to find a contradiction in Relativity then you have to play by the rules.
LT does the same thing. That is what I showed you.
However, if you are going to suggest SR cannot conclude this type of distance measurement, then you must say that is not logically decidable under SR.
This implies there is a simple problem in motion and measurement that SR cannot answer and thus, SR is an incomplete theory.
Also, if you conclude this, then I will break LT and prove its claims are not logically decidable.