Dear Ron,
Thank you again for asking all the right questions in your essay.
Regarding the nature of the quantum wave, here are some other key questions:
Does quantum diffraction really prove the presence of quantum waves for all "particles"? Are all particles the same?
I argue that quantum diffraction is not classical wave diffraction at all, but rather a discrete transition that changes the momentum of the "particle" by transferring quantized momentum from the lattice or slits.
So a neutron can be a small particle on the 1-fm scale, but it can show quantum diffraction effects from a crystal lattice that would appear to require a coherent wave on the 1-nm scale. No such wave exists.
On the other hand, the electron is a true de Broglie wave packet, as shown by obeying the Schrodinger wave equation. But it, too, can produce quantum diffraction effects, even without long range wave coherence.
Similarly, the energy of a vibrating molecule is quantized, and this is usually taken to prove that the component atoms are waves. But in fact, atoms are real quasi-spherical objects undergoing classical oscillations. The energy is quantized only because transitions are mediated by photons, which themselves are quantized wave packets. Only certain classical trajectories are accessible.
If you are interested, I can give you some citations that discuss these issues.
Alan