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Anton, thanks for reading and commenting.
Actually though, I do see physics without atomism as a physical world without atoms (which are quite distinguishable from field quanta, which we can certainly allow). Not only that, I also see physics without atomism as a physical world without a physical space which exists without matter in it - that is, without space as either a "theater of operations" or as an actor in its own right (although we may certainly allow spaces in the mathematical rather than physical sense). It really is only an argument for a background independent field theory, which is not really very outrageous - GR is already such a thing.
I think (at least I hope) that my essay explains clearly how physics, especially quantum theory and the process of unification, would benefit if we were to eliminate both localized particles and background physical space.
To relate a little to the theme of your essay, I would say that I do not think is sensible to say that empty space has a geometry. Empty space is the absence of anything, and therefore of any characteristics. We cannot travel 1 light-year through empty space, spend a fortnight in empty space, nor scoop up 2 cubic meters of empty space, nor for that matter even identify a point in empty space. I can certainly agree with the theme of your essay that new physics might require both new physical laws and new geometries, however I would simply argue that those laws and geometries should describe a continuum - a field - rather than a localized particles and space which somehow exists and has properties, even a geometry, without anything in it.
Best of luck and thanks again for commenting.
Mark