Steve,
"Why are these things any different from things we already have?"
Aaahhhh... I'm very glad you asked that.
Answer: Because they aren't!
I'm not saying the analytic geometry isn't right, I'm saying; that's what it is. It is just Pete presents it as a model, which it could be if it were in a reference frame of Minkowski 4X4 matrix Blocktime, then the helix could physically operate like an apple peeler stripping off helixes of disturbed spacetime. But it only infers a physical model (the link sausage string made by the helix pudding machine) by projective trigonometry, the time and energy have to be put in by hand. In that sense it is not a model itself, and I dislike 'framework' unless it ontologically exists as the armature of a model of physical material properties. It is rather the same genus but different species as Einstein's GR construct. It's not a theory (though many theories might come of it) and its not a methodology; it is a mechanism, you apply your own method to it.
Pete, you might consider pitching it as a mechanism, and calling it the Discrete Field Mechanism. And here's is why, Steve..
As a mechanism it can project a physical model, while as an analytical geometric mechanism it can project vectors trigometrically without interaction physically, non-locally. But those vectors are relational to the helical parameters, the point on the helix incident to projection is the point at unity of coefficients between the helix parameters and those of the "Tiny spinning gyroscope" . Simple right angle induction, point at unity of time , physically it could amount to magnetic traction, but skids at 45 degrees. That sort of interface, its a mechanism. BUT TRANSLATIONALLY, that sets the vector given the proportions of coeffecients; the induced anglular attitude of the axis which is 'direction' (okay... you get to be the quarter, I'll be the twist-off beer cap with the horses head on it, both turn out the same unless we say so) and the size of the disc is 'magnitude' being equal in length of axial and diameter in proportion to helical diameter. It's a vector projector.
So what ontology might be had to relate those projective vectors as quantum vectors? I can think of a QTD = quantum time density, completely ad hoc. Relative inertial energy density, could be a parameter. Pete's prohibition against anything other than helical (or distortion thereof) being translational of wave mechanics is simply axiomatic, its a mechanism. Can it be Quantum as well as classical?
Peace out jrc