Those 'precision EUV mirrors' achieve a reflectance of about 70% i.e. they aborb ~30% of the EUV light that reaches them. :)
More seriously, those mirrors are special because they use bragg reflectors to handle 13.5nm light. They're not special for their precision, nor their reflectance.
Setting that aside, the major problem with your proposal is that laser still have significant bream spreading. So the mirrors would need to be large enough to encompass a spread beam at every step, which adds weight and volume for both the mirror and the tracking mechanism. The tracking mechanism is particularly problematic because moving mass on a satellite affect the attitude, so you either need precision counterweights to null it out, or large reaction wheels.
Using MEMS mirrors instead would solve some of the mass issues, but MEMS mirrors have very limited tracking (typically limited to a single axis) which would probably render them impractical.
Far, far easier to just send and receive the signal at every step.