How to properly relate quantum mechanical energy to the classical world
*So we cannot stop here as quantum theory and classical mechanics are virtually indistinguishable (with respect to raw energies) at this point correct?


This is wrong. Just because you can't immediately, instinctively comprehend the difference between the $10^{-18}\  \mathrm{J}$ and $10^{-71}\  \mathrm{J}$ and therefore think they are both "indistinguishably small" doesn't mean it's true. The difference is massive. Our brains just haven't evolved to deal with numbers whose logarithms are very far from 0, because for almost all of our existence as a species, it never had to. Perhaps this site may give some very qualitative though fun context on how brains perceive the magnitude of a number.

In order to cope with this limitation of ours, we have developed some strategies. One can be understood as a form of chunking, where we simply modify numbers in a way so they become closer to something we understand. You probably won't be able to immediately give an example of an object that weighs 200,000 ounces or $3\times 10^{-27}$ solar masses, though you may find it quite a bit easier if I say 6 tonnes instead. This is because even if we inherently know the concept of an ounce or a solar mass, we can't really comprehend the magnitudes of 200,000 or $3\times 10^{-27}$ (the latter of course being much worse), and in order to get our heads around it more easily, we instead invent a new unit to measure weights in which we can express the same information using numbers closer to 1. The whole idea of scientific notation for numbers and SI prefixes for units can be understood as a consequence of this.

Another way is the one you use; instead of reframing the units and numbers, reframe the situation. You may feel there is no difference between $10^{-18}\  \mathrm{J}$ and $10^{-71}\  \mathrm{J}$, but the 53 orders of magnitude in difference is about the same as the number of atoms in a human body and the number of atoms in the entire observable Universe! Notice how I simply took the ratio into a slightly more familiar context (you know the Earth is just a small part of the observable Universe, and a human being is puny in comparison to the Earth).

So all of your calculations are correct, but if Homo sapiens were smarter, they would be entirely unnecessary!