I have no idea what your talking about or where this is all coming from. Getting to hard to have two conversations at once. I think that there is length contraction in the other frame so that the beams of light in the MME will reach the detector at the same time. Then they will measure the same speed of light in both directions, the added distance it has to travel in the direction of motion is shortened just enough so that it is seen as being the same distance from another frame. Same speed, less distance traveled, with less time then counteracts the longer distance the beam is seen to travel from another frame that would think it would have to travel a longer distance since it is in relative motion.