Jeffrey,
I enjoyed the way you started off with Magritte's "This is not a pipe". I often quote Alfred Korzybski, in 'Science and Sanity', who said "The map is not the territory." He seems to think that recognition of this is the key to sanity. I do believe that, in today's physics, there is more confusion between reality and representation than perhaps ever before. So I applaud your focus, in your title and your opening paragraph.
I also like you point, "A fundamentally discrete universe will have a scale level where energy or position can have a level of one or two units, but not one and a half."
I was not quite sure about the diagram until I read your comment to Juan above, that "I do have a little diagram showing how a quantized universe is impossible, but I did not make it a clear main point."
And I agree that teaching is the best way to learn. When I used to teach I could tell by their eyes that the students did not understand, so I found another way to explain. If this didn't work, I looked for another way. Often, I had never seen the third way myself, so at least one of us learned something.
You may like to read my essay. It agrees with you that the fundamental nature of the universe is analog, with thresholds such as Planck's constant and the speed of light that provide separation and hence a degree of discreteness.
Edwin Eugene Klingman