I don't think Godel's theorem addresses the Illuminist's ontological claim that reality is made of math. The theorem says only that no formal system can prove the completeness and consistency of all math, so that seems to be a limitation of our knowledge of math. Mathematical systems can formulate paradoxical, self-referential statements that can't be formally either proved or disproved.
This is accounted for if we understand math as being game-like and based in the imagination, as I suggest in the article. We can imagine more than we can prove or know. Does that mean the world isn't fundamentally formal? I'm not so sure. Then again, I'm no mathematician.