I mean, to be honest, the etherals seemed a little... shifty. I dont think thy were just looking for a replacement race. We wouldnt have to fight that hard to prove it. I think that was their last-ditch attempt at survival.
I haven't beaten NewCOM 2 yet so I don't know what Avatar is. But... I feel pretty confident about my interpretation of NewCOM 1. The Ethereals served some unknown entity that wanted a perfect race, a blend of psionics and toughness. The ethereals failed, they were too frail. The other races failed due to insufficient psi power, or the sectoids being weak in body AND mind. Human DNA seems to hit some idea middle ground, one they were unable to reproduce (by, saying, mixing a muton with a sectoid or ethereal).
So they wanted our genes. That's why they abducted so many people, and experimented with human psionics. Their human psi captives had abilities beyond even the Volunteer, by the way.
After NewCOM 1 I thought they wanted humanity as a slave race, mostly intact except for some tweaks. NewCOM 2 goes in a different direction - using those amazing human genes to enhance the existing races, most notably the sectoids. I get the impression that new sectoids are almost half human, even. And I'm sure the Avatar project is a continuation of that, some sort of ideal human-alien hybrid with JUST the right mix of physical stamina, reflexes, and most importantly psi ability.
Again, I'm pretty sure it's this timeline's version of the Volunteer.
I'm tempted to let my current, very suboptimal run fail. Just to see what it looks like. Though I bet they don't actually show it off much in the failure ending...