Dan,
I liked your essay because the central idea was clearly stated and made a connection between two concepts (particle number, precision of particle position) in which infinities could conceivably appear which might not have been obvious otherwise.
The only quibble I have is that the fundamental lesson of relativity is that spacetime, not space, is fundamental, and your essay still seemed too much tied to the pre-relativistic viewpoint. I believe this is only a minor objection as this argument should be adoptable to a four-dimensional version without much difficulty, although then some additional subtleties (non-conservation of particle number, finite age of the universe etc. ) may make for a richer discussion.
Good job and best wishes,
Armin