In which point the Aether Wave Theory goes against mainstream? We know, the Aether concept is considered a pretty well abandoned idea.

The main difference is, the classical Aether theories have described the Aether from perspective of thin gas. This was a typical misconduct, because the light of high energy density cannot be mediated by very thin environment. Aether Wave Theory therefore extrapolates the behavior of ultra-dense inertial systems, like the interior of dense stars and black holes. Surprisingly, very low number of scientists so far have interested about inertial (Newton) physics of high density matter.