Stephen
I found little ontological basis for resolution of some of the knottier problems in rationalising observation, and am unable to comment on the veracity of your maths, but the brilliance and veracity of your findings as far as they went shone out so brightly that the above fell into the shadows. I sense a high score coming on!
You will find an ontological analogue of your essay in mine, from a slightly different vista (and language) and lacking most of the essential mathematical basis you provide, though extending to address matters of Unification, Space-Time etc. As an astronomer I also find significant astrophysical falsification.
You'll find a number of other consistent essays here, including Kingsley-Nixey who reviews and lists others.
I critically agree your observation that "Lorentz covariance applied to time and spatial relationships is too restrictive as a constraint to be generally applied to field expressions for elementary particles or to serve as an underlying basis for their determination."
You may not recognise the view from my approach immediately, but quickly will. I use Proper Time rules and delta lambda on detection, analysing frequency from different observer frames and deriving two distinct cases instead of the assumed one, of more than one phenomena.
I'm very interested in whether you found the same commonality as I, and of my own basic formula conserving c, energy, (and the wave'function') locally via the Doppler formulations. I'd also like to identify any present divergence.
I hope you don't mind Shakespeare!
Best wishes
Peter