Timothy.
"It is still an open question as to how much of Nature can be described in terms of classical physics which includes classical electromagnetic zero-point radiation."
Perhaps not for much longer. You've just lit up some dark areas I've been exploring naively and ontologically from very different approaches. I expected to understand little of your essay, but rationalisations of my own findings of an 'underlying physical basis' abounded; i.e.
The motion of Earth through the Barycentric frame (still problematic).
The boundary conditions on Maxwell's equations.
'...it should be Lorentz invariant and scale invariant.'
h as the multiplicative constant setting the scale (of random classical zpr).
...quantized free fields or quantized harmonic oscillator systems.
The balance between pick-up and loss leads to equilibrium for electrons.
Motion in Coulomb potential in ZPR doesn't allow analytic solution. (try Navier-Stokes!)
...spectrum invariant under scattering by a relativistic scattering system.
non-inertial frame; assumption that correlation function for random em field involves only the geodesic separation where the field is evaluated.
...thermal bath at a temperature proportional to the acceleration (the Unruh effect).
The particle interference effects when particle pass through slits.
...electron in a finite-size orbit picks up and loses energy at not just the fundamental frequency but at all the harmonics of the basic frequency.
And very many more areas where I hope you may also obtain a fresh view from my own approach. My essay discusses only some kinetic fundamentals and effects as the tip of the iceberg I've explored. You'll not be familiar with the language, but focus on the logic and findings. You should perhaps first look at my current discussions on Eckard Blumshien's essay blog, where I explain the central relevance of scale invariant surface magnetohydrodynamics as a boundary condition. See also Fig 1 of Richard Kinsley Nixey's essay, and consider this in terms of a local non-inertial frame. I hope an overall ontological framework will appear, consistent with your own excellent work.
The concepts were also discussed as a 'Discrete Field' model (DFM) in previous essays here (i.e. 2020 vision 2011). Solutions for many astronomical and other anomalies and paradoxes have emerged. In terms of unification, SR emerges direct from a quantum mechanism, and it seems even Copenhagen can be re-interpreted classically!
I won't flood you with more links to papers for now.
I look forward to discussing more detail.
Peter