Dear Franklin Potter,
It was interesting to know how a veteran, still in the game, views the unfinished game. You say, "I argue that this j-invariant connection dictates the lepton mass ratios to be 1:108:1728, values very close to the actual charged-lepton mass values 0.511:105.7:1776.8." Thus, in fact, what you have provided is just a correlation between mathematics and physics at the particle level. Can this be sufficient reason to assume that 'fundamental mathematics dictates the fundamental physics'?
A mathematical relation can have different physical interpretations. The difference may be sometimes very thin. I would explain the above relation as follows: 'Given the fundamental properties of matter, mathematics dictates the structures'. Regarding laws, my opinion is that the physical world has no laws of its own. The laws applicable to it are mathematical, and these are "eternal and absolute".
You ask, "Have I convinced you that the fundamental particles as well as we humans are mathematics instead of simply being described by mathematics?" Here also a slight change: Given the fundamental properties of matter, the mathematical laws dictates the emergent structures, and now human structures are present in the universe (the laws not just describe, but dictate).
I request you to read my essay A physicalist interpretation of the relation between physics and mathematics and visit my site finitenesstheory.com. I would appreciate your comments.