To ultimately sum up the above work, it says: The universe is Infinite.
Math is an approximation by its very nature. For example, if we attempt to determine the movement of a planet around the sun, if we don't account for other planets we will be inaccurate. If we account for other planets, we will increase accuracy but we will still not be accounting for other systems. As the universe is infinite, it is impossible to account for all infinite systems. So, yes, I would agree that it is impossible to write an equation or set of equations that encompasses all that is. However, that does not preclude us from recognizing the universe to be the manifestation of infinity.
Regarding the Vedas, they are a portion of all that is. Like any portion of all that is, they contain a portion of the truth. But no single portion of all that is contains the whole truth; that is reserved for all things as a whole. While there are truths in the Vedas, many are not even able to be extracted without careful consideration of a large enough spectrum of sources so as to understand the universe's Infinite nature.
Quantum theory is an invalid model that violates exactly what you mention of the incompleteness theorems. They attempt to contain within a single set of equations the entire fundamental workings of the universe, and in so doing they are inherently built as an approximation that falls apart with ease the further from the source of approximation an observation is. They do not recognize the infinite structure of the universe and as such cannot in any way describe the universe, as it is the manifestation of infinity.
The Vedas are certainly of value and I agree that they contain vast wisdom. However, they alone do not contain all the knowledge of the universe because they, just like an equation, are a limited part of all that is and create only an approximate picture of the infinite universe. When only one source is looked to for information, it produces a skewed reality that is limited. As such, individual sources of information are effectively incapable of capturing the full extent of truth. This even includes individuals such as myself. I do not claim to know everything, but this theory is instead the cornerstone of understanding upon which an infinite progression in knowledge can be obtained without approximation. It is the beginning of understanding rather than the ending.
RE: The True Theory of Everything: Link Compilation