I'm with you about 80% of the way here.

Godel showed (and guys tell me if I mess this up) that formal self-consistent systems have both statements that are true that cannot be proven and false statements that cannot disproved. In other words, complete systems are incomplete.

This does not mean that complete systems cannot model reality to a high degree -- there's no reason why a ToE could pop out from some rotation or transmutation of mathematics. It just means there would be parts of it that would be incomplete -- the model itself could have a very high degree of fidelity.

When applied to higher math and physics, this is another way of saying "you don't know what you don't know" ie, the models can work perfectly across all observation space and still be true to Godel.