Dear Blake,
Although you say you were pressed for time while writing this, you nonetheless present some very worthwhile ideas, and express them quite well. You also seem to have the mathematical maturity to make these ideas precise. A couple of thoughts.
1. Since Weyl was one of the fathers of representation theory, I thought you might be interested in a different take on this crucial subject. Many approaches to quantum gravity involve nonmanifold structure at small scales, and this makes the use of covariance in the form of the representation theory of the Poincare symmetry group difficult for determining particle states etc. However, one can alternatively view covariance in order-theoretic terms, and this viewpoint is much more general (see my essay here On the Foundational Assumptions of Modern Physics for more details). This opens up the following interesting question: if you use something more general than groups, what do you do about the representation theory? It is also interesting to think about gauge theory in analogous terms.
2. A couple of other essays here that might interest you are the ones by Torsten Asselmeyer-Maluga and Jerzy Kroll. In particular, they involve exotic smoothness structures, which can accomplish some of the same things as magnetic monopoles, among many other interesting properties.
Take care,
Ben Dribus