A very concise well written essay Declan - congratulations. It does seem that there is growing awareness that matter is made of waves, and that these waves propagate through space / aether (an absolute reference frame).
You have shown how this foundation deduces relativity correctly without the strangeness - and this is very important for the sensible evolution of human knowledge.
A few thoughts (from a philosopher!);
i) You talk about matter waves and light waves as if they are different things. I think you will find that light waves are really just patterns of hills and hollows on the surface of the plane waves that form matter (I will discuss this at our WSM group and try show a diagram some time soon.)
ii) You have time dilation, yet if what exists is waves in space, then time must be due to this wave motion, thus time dilation must really be caused by a change in wave velocity. I am curious, if you keep time constant (same as keeping frequency constant), and just have the wave velocity and wavelength changing do you get the correct results?
iii) I agree that gravity must be due to a slowing of wave velocity in higher energy density space, thus the curvature of light past the sun is really a classical diffraction (what Einstein called the curvature of the 4D space-time continuum).
iv) Do you have thoughts on charge? My view is that this is also caused by variable wave velocity, where higher wave amplitude waves have higher velocity.
Good luck with the contest.
Geoff