Hi Peter,
Thanks for the comment and questions. You're right-- the essay is packed with info (some are truisms, but in QM even that is debatable.) To deal with a century of confusion requires covering a lot of ground in 9 pages. You ask whether I think 'probability' may be just the incomputability of complex interactions beyond our capabilities. In the essay, I use the 'partition function' of statistical mechanics as the basis of probability for energy states and then show how this links to the physical wave (length) to allow the calculation of probability amplitudes. The partition function, which is typically based on huge numbers of combinatorial events, probably meets your specification as to the nature of probability. What I focus on is the generally-not-understood connection of the physical wave to probability wave (as Dirk Pons noted above).
I have not focused on Heisenberg and diffraction (I count on you for that!) but I generally view Heisenberg in two compatible ways. The finite wavelength lends itself a certain Fourier-based limitation that can be considered 'uncertainty'. Also, in previous essays, I have derived a quantum flow condition that generalizes his relations. In any case, the existence of a quantum of action strongly limits what can be measured without disturbing the system. I reference recent Aharonov-based 'weak measurements' that get around this limitation, but only statistically.
Your question about a dozen particles on a motorway is good. In my opinion the wave 'phase' associated with each particle is inherently unknown (unmeasurable) so exact calculations are impossible, leaving us with a distribution of 'most likely' values as you desire for your "derivation of SR from a QM."
My essay shows how one can understand quantum mechanical probability amplitudes from physical waves. Lack of information on individual phases means that probability is the best we can hope for, but this does not imply the mystical consequences that follow from belief in the pure 'probability wave' that has characterized most quantum interpretations for a century.
Thanks as always for your insightful questions.
Edwin Eugene Klingman