Dear Stephen,
I have read your interesting paper. I did not understand every technical detail, but the main message I hopefully got, that is, the Lorentz Invariance in its relativistic version is too restrictive if applied to space and time.
I discovered a space-time-picture that is less restrictive, but its inner design follows nevertheless a specific type of Lorentz invariance, that is slightly different from the relativistic version. The underlying space-time-picture is geometrically composed of a SQUARE and a CIRCLE, both blueprints are closely entangled to each other.
This somehow archetypal space-time-picture implies some interesting features. One of the most important features is the existence of two faces of c; a feature, what I am calling the DUAL PARAMETRIZATION of C. It means, there is a particle-like face of the constancy of light - and there is a wave-like face, too. As both faces are formally parametrized in the same way, i.e. c = 1, it is almost impossible to recognize the particle-like face of c. It is still hidden.
The relativistic kinematics is actually insensitive with respect to this Dual Parametrization of c. It is not only compatible with the wave-like version of the constancy of light as it is stated in the second postulate of SRT, but it is also compatible with a particle-like version of the constancy of light c.
In his 1905b-paper Einstein has noted that the velocity of light V cannot be altered by composition with any subluminal velocity but he did not see its full meaning with respect to the speed of light. John Stachel was wondering about this. He asked himself: Why did Einstein not note this possibility though it must have been equally obvious to him.
Reference: Stachel, John. Einsteins Light-Quantum Hypothesis, or Why Did not Einstein Propose a Quantum Gas a Decade-and-a-Half Earlier? (Einstein. The formative Years, Einstein Studies 2000, p. 240)
This kinematical notion - if connected with a particle model of light - implies a far-reaching experimental consequence : Even if the speed of light depends on the speed of the emitting source, the speed of light would always be measured as c = 1.
Consequently, all experimental tests concerning the second postulate of SRT are not unambiguous. There is - at least in principle - the possibility that something different has been measured - a sort of a particle-like version of the constancy of light.
May be you find this view interesting..
Good Luck for your Essay.
Kind Regards
Helmut