Far from MiHsC being antagonistic to (special) relativity, what I am doing with MiHsC is going back to an attitude that you might call 'What can't be seen, doesn't exist' or 'What you can see is what you get' (WYCSIWYG) that has produced most of the great leaps forward in physics, including Einstein's special relativity.
The first example of this attitude was Thales way back in 600 BC who rejected ancient Greek mythology and insisted on modelling nature with something that could be seen. OK, he came up with "Everything is water" which was easily falsified, but this is the crucial point: the idea was falsifiable, and so Thales started the scientific process (dark matter and string theory are not easily falsifiable and are not good science).
Newton used this attitude when he rejected Descartes' model of gravity which used unobservable vortices, and when he derived his theory of gravity he focussed on things that could be measured like masses and distances and refused to hypothesise about what gravity might actually be since he couldn't think of anything that could be tested. However, he faltered when he introduced the invisible entities of absolute space and time which can't in principle be seen, and was later critised for that by Gottfried Leibniz, Bishop Berkeley and most especially Ernst Mach. This idea of focussing on 'observables' or things that can be seen is sensible, in the same way that crossing a river using the most solid-looking stones is sensible.
Einstein had read Mach's criticism of Newton's unobservable space and time and decided to devalue them and focus on something that could be seen and tested like the properties of light. This had consequences. For example, if you have a couple of mirrors and you get a photon to bounce up and down between them, then this makes a sort of clock. Now if you happen to see this clock moving sideways past you, then from your point of view the light has further to travel because it has to move along a diagonal path, but Maxwell's equations say that the speed of light is always the same, and this has been experimentally confirmed, so the clock now must tick slower as it takes longer for the light to go along the diagonal. Some might say this is just an 'appearance' of slowness. Einstein was happy to say that time has really slowed down, because time is not a thing you can measure well from a distance anyway, whereas the constant speed of light had been well measured, so it made sense to believe in the properties of light and be flexible with time. This implies then that physics is determined by what you can see (and this does not mean by us as individuals, but what you can 'in principle' see). This was confirmed experimentally by Hafele and Keating (1972) who took one clock on a plane trip round the world and showed it slowed down relative to a clock they left at home.
MiHsC is based on this same observable attitude, but now applied to the new discovery of information horizons. You can make such a horizon if you suddenly accelerate, say, to the right. Then, information from a certain distance to your left can never catch you up, being limited to light speed. The boundary between what you can and can't see is called the Rindler horizon. There is also a cosmic horizon, because objects at the Hubble edge are traveling away from us at the speed of light and we can't see them, or what lies beyond.
So with this attitude we must assume that from the point of view of someone accelerating there can be nothing beyond the Rindler horizon they see behind them, because they can in principle see nothing there. Also from the point of view of someone within the cosmos, there can be nothing outside the cosmic horizon. This includes fields, so all fields must have a node (zero value) beyond the horizon (fields can't wiggle in nothing) and also on the horizon. In this way the cosmos is like a drum in that all waves on it must close at the boundary and only some vibration patterns or 'notes' are allowed.
In MiHsC I assume that inertia is caused by Unruh waves, and so this attitude means that these waves too can only exist if they have nodes at the horizons.
It turns out that if you do assume this, then with the Rindler horizon MiHsC predicts the standard inertial mass to within 29%, and also with the Hubble horizon it predicts a subtle deviation from the standard inertial mass that agrees with the anomalous rotation of galaxies, galaxy clusters and the recently observed cosmic acceleration. It also predicts the low-l CMB anomaly, an anomalous suppression of patterns seen on the longest cosmic scales, and several other anomalies, including emdrive.
My general point is that whenever science has focused in on things that can be 'in principle' seen, it has leaped forward. Whenever it has lost discipline and used non-falsifiable things like epicycles, vortices, strings, extra dimensions or dark matter, it stagnates. MiHsC represents a new era of focusing on observables, like the period from 1899 to 1930, and sure enough it predicts anomalies that other theories can't reach, without having to invent invisible stuff.
Hafele, J.C. Keating, R.E., 1972. Around-the-World Atomic Clocks: Predicted Relativistic Time Gains. Science, 177 (4044): 166–168.