Dear Abhijnan,
It's tremendous to see an essay here involving algebraic geometry and K-theory. You present a lot of interesting ideas, of which other physicists should take note. A couple of questions/remarks.
1. I know that the string theorists are already trying to apply K-theory to things like D-brane classification. I think it's mainly the Milnor part that's involved, and hence motivic cohomology, which is right along the lines of what you suggest. I don't know a ton about string theory, so I'm not sure how far they are along.
2. Do you have any specific dynamical ideas accompanying your suggestion of K-theoretic atomic decomposition. "Chow ring dynamics" would be fascinating and would draw more outside attention to the study of cycles.
3. On the subject of the Chow ring and the cycle class maps, Green and Griffiths initiated a program of study involving the infinitesimal structure of the Chow ring which is interesting and will hopefully prove useful. It involves the Gersten resolution of the K-theory sheaves (whose sheaf cohomology yields the Chow groups) and a "tangent map" to relative negative cyclic homology induced by the relative Chern character (they don't describe it in this language, but that is what is really going on). My thesis advisor and I have developed this theory somewhat further. I have not thought about it as a way of studying fundamental properties of spacetime, but your ideas prompt me to take a second look at this.
4. I read Connes-Marcolli a while back, but not very carefully... my impression was that they were actually quite modest with their claims; I remember they suggested that the 6-dimensional noncommutative part of their spacetime model together with the 4-dimensional commutative part might relate to the "more fundamental" 10-dimensional string theory space. They also made an incorrect "prediction" of the Higgs mass, but I think the attendant assumptions were such that this wouldn't invalidate their general approach in any way.
5. By the way, my own ideas about fundamental physics up to this point are very different than my math work; if you are interested, you might look at my essay On the Foundational Assumptions of Modern Physics. Noncommutative geometry plays an important role, but not so much continuum manifolds or algebraic schemes.
Again, I enjoyed your essay, and wish you the best of luck with the contest. Take care,
Ben Dribus