Dear Jose P. Koshy,
Enjoyed your essay, very thought provoking "A Theory of Everything will indeed be a physical theory, explaining the physical world in physical terms. Everything will be explainable on the basis of fundamental properties that are stated in unambiguous terms having physical meanings." This is a description of what inspired my work on this essay contest.
I liked your conclusion "The point raised in this essay is this: The physical world should be explained primarily on the basis of physical-logic. Mathematics has only a specific role of deciding how the world changes with time."
Hope you get a chance to look at my essay as I think you will see a fair amount of physical logic with physical meanings in modelling the mathematics behind the fundamental particles.
Many regards and good luck,
Ed Unverricht