Dear Jonathan,
Good to see you again here. I thought I had written earlier on your essay, but I now see why I didn't. Our views are almost orthogonal, so it makes little sense for me to critique your essay. But it is good you present the Platonic view of math, as I try to present the Realist view of physics. Thus those who are undecided get a chance to ponder both views of reality.
There are some excellent essays (as usual) and I count yours as one of them. I particularly like the following:
"I'm sure nature is perfectly happy with processes taking more or fewer stages to complete, but the math itself dictates that certain patterns are more stable than others."
I think that works from both of our perspectives.
Best wishes to you, and as our mutual friend Ray Munroe used to say:
Have fun,
Edwin Eugene Klingman