I do know the calculations and you are definitely correct. :-)
From my point of view, the universe revolves about me. Don't need no calculations!
Hold on. Doesn't have to be "far above the ecliptic." It just has to be geosynchronous. Then it's always making observations w/r/to the earth's position. It would mimic our own observations. What's wrong with that?
My instinct--what, you're expecting calculations here?--is that there's no such stable orbit as "far above the ecliptic" and "fixed in position wrt the earth."
I do know the calculations and you are definitely correct. :-)
But couldn't you shoot a probe far above the ecliptic, in an "orbit" that's fixed relative to the Sun, and another fixed relative to the Earth, and then see which one takes more fuel to keep itself in position? Seems like that should be a valid proxy for finding the true "objective fixed observer". (Recognizing that the solar system itself is in transit towards - Vega, is it?)
Just what would a "fixed position" mean, anyway? Some least-squares summation of change in vectors between the object and every other visible object in the universe? (Or at least a representative sample of stars in this galaxy?)