Hi Leo,
"If I can't picture it, I can't understand it." This sentence is attributed to Einstein by physicist J. A. Wheeler in John Horgan's article "Profile: Physicist John A. Wheeler, Questioning the 'It from Bit'". Scientific American, pp. 36-37, June 1991.
Probably your and also my understanding of the first steps in physics is similar. I does not matter that our detailed concepts are quite different. And by the way: I admire your graphics!
In your essay I can see something deep and true (in my opinion) in the approach itself: the mystery of Reality lies in geometry. Even in biology or rather biochemistry the shape is what decides if the reaction will happen or not. E.g. in every cell of an organism there is a lot of chemicals but reactions happen sporadically. The increase in rate of a chemical reaction (a tangible effect) can happen only due to the participation of a substance called a catalyst. The catalysts simply have the proper shape that fits to the other shapes. They are called enzymes - selective catalysts, vastly accelerating both the rate and specificity of metabolic reactions (e.g. the digestion of food or the synthesis of DNA). And most of them are proteins.
Nevertheless if I could advice you anything: do not underestimate the abilities of mathematics. The same Einstein said: "Thoughts and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment"
Regards