Dear Michele, nice read and nice work – congratulations!

However, let me point out one of the issues most people have with 'quantum mechanics': semantics.

I was also wondering about this in the first part of your text, when you stated that you started by looking at physics 'observables' such as bond distances, etc. Which are of course a very classical picture of a molecule;-) Does the "distance of two atoms" operator correspond to a useful observable of a polyatomic molecule? Does it actually commute with the Hamiltonian?

The fact that nuclei are delocalized is obviously a very old concept, i.e., as old as quantum mechanics itself. It's observation goes back to (before) the umbrella inversion in ammonia and was, for instance, exploited and understood in the demonstration of the MASER by Townes and coworkers in the 1950s. A very instructive/pedagogical paper on this, with analytical 'descriptions' and many nice wavefunction & nuclear-density pictures is this article in the Journal of Molecular Structure (1972): https://dx.doi.org/10.1016/0022-2860(72)87050-9 (I am sure there are earlier and better depictions, but this one was instructive for me at some time;-)

Now, I still like your careful analysis of how far empirically adjusted classical physics can go for such quantum objects as molecules and look forward to more people realizing the need, opportunities, and beauty of (molecular) quantum mechanics.

Best wishes for pushing this forward:-)