Ian,
Lovely essay, well presented and pertinent with some important truths but I have to suggest some key propositions are flawed.
Your use of 'probability mass' was novel if rather cumbersome. Correct of course (I asked Marylin!) but a better and clearer Cardano 'sample space' was long ago derived which you rather muddy in re-inventing. Indeed even Wikipedia is wrong on this stating origins from the 1800's (Google 'Monty Hall'). Cardano was born in 1501.
Applying sample space to 3-axis oscillations isn't so much an issue as wrongly assigning the outcome as "due to maths". Your; "almost entirely mathematical" is at least a small step back, and credit for; "After all, the mathematics refers to something physical." Which rightly contradicts the earlier error! I can see what you were getting at, but that thinking is what misled all the top maths PhD's to be embarrassed by Marylin dos Savant.
I suggest, in line with probability theory, that ALL 'chance' can stem simply from a 50:50 coin flip or particle x axis orientation with respect to an interaction (all fermions in space and particles from a splitter either present North OR South poles to a detector/observer (D/O); 50:50 (unless modulated to a common direction in a field at the D/O) with MAX UNCERTAINTY AT A SPIN EQUATOR!
We could then say your statement "the shifting of an energy unit from one oscillator to another. This microprocess is fundamentally random" is erroneous, but could also say it's correct IF the randomness is derived from the above at 50:50 (and think 'electron', or even; 'Majorana fermion'!). Which you should agree it can.(??)
Now something new I propose; In 'OAM' there are TWO distinct momenta states (as Maxwell) which may be transferred on 'contact' (or absorption/re-emission). One is the UP/DOWN at the equator. The other is the 'curl' at the poles. These are then then orthogonal and vary 0 to 1 non-linearly by the cosine of the 'latitude' on the interaction point on the sphere surface (a fact you'll find hidden away in geophysics).
I suggest your paper does get part of the way there, going rather off track, but then does give a pretty good overview of how QM can actually be derived deterministically (classically) down to a reducing fractal uncertainty.
Of course your model doesn't raise cognative dissonance where a more Classic QM does, so will doubtless remain dismissed!
I'd be interested in your views if you get a chance to study my essay better explaining the model and it's ('multi layer' space) derivation 'aims and intent'.
Very Best
Peter