I am in a space-craft moving at .99c observing the Michelson-Morley experiment. I am perpendicular to one of the interferometer 'arms'. Due to the apparent 'reality' of Lorentz length contraction I would now see a different expected deviation of the interference fringes perhaps large enough so that it would now seem to confirm the existence of the 'aether'.
Think of the MM experiment as comprising a longitudinal light clock, a transverse light clock, and a sensitive way to compare their rates.
Once think of it that way, you can see that the MM null result Is true in any frame of observation. Both arms change rate in the same way, so the comparison always gets the same answer.
Lorentz length contraction is the consequence of the invariance of light speed in all inertial frames. When you say that you would use this fact to prove that aether exists and light is a wave in this media, the length contraction doesn't work anymore.
You are mixing one theory based on non-existence[*] of the Aether to prove Aether exists, that is simply not possible.
[*] To be exact: Not on its non-existence, but on its non-importance for the propagation of light.