Dear Don,
it is true an elephant is running around in modern physics. But how does this elephant look like? I am sure you know the story of the blind men and an elephant. It has often been used to illustrate a deficit of information and the need to accept different perspectives.
What is the ultimate truth of the Universe? Are its internal processes moving in a digital fashion or are they moving in an analogous fashion?
I think, we still tend to solve this riddle by make a decision in favour of one of these two possibilities and against the other one... But perhaps every one-sided view (including in its most subtle and sophisticated version) is a fundamentally limited view, that does not cover REALITY in its totality.
Though I believe, that your approach is physically fruitful and promising, it does not touch the deepest level of reality. I am convinced, that velocity v = Delta_x/Delta_t is valid from v = 0 until v = oo without any exception or gaps.
This continuum is indeed the underlying branch to make statements - the term of velocity is only valid as long as Delta_x and Delta_t are not smaller than the deBroglie wavelength and period of the particle being - meaningful at all.
This continuous or analoguous spectrum of velocities may still be considered as a metaphysical assumption of physics, but it is to my opinion its central core. The real weakness of this assumption is still its implicit character: We think WITH them and not OF them. (Michael Polanyi). Therefore I am looking for a Modern Metaphysics.
I left a comment on my FQXI-site, too.
Good Luck for your Essay.
Kind Regards
Helmut