The model of reality is created by and used by your mind, and your mind is part of reality, so already that catch-22 intuitively precludes the model from being provably correct and complete even if your mind could somehow be completely unbiased and objective in every other way (which our minds aren’t, our biases and preexisting beliefs and feelings inform physical theories and models all the time).

I don’t see why your approach is not subject to the same limitations.