No ET! Ever?

[Anomalocaris]

Your moving target over interstellar distances is effectively static; the stars are in pretty much the same positions as when they were observed by the Greeks / Ancient Chinese.

That's false:



And, the above is not accounting for the proper motion of stars throughout the Galaxy. 

    

That picture you show reflects the precession of equinox.   It does nothing to change the relative positions of each star, nor increase the difficulties of targeted transmission to stars. Also, I believe the ancients regarded the heavens as being immutable in the celestial sphere, not immutably oriented with respect to earth. So the ancient's concept of where stars are would be relative to other stars, not to their location relative to the horizon. So the idea that stars seen by the ancient Greeks and Chinese would still be in pretty much the same positions is accurate. Proper motion would have made very little difference for most stars in the intervening 2000 or so years.