Whoa. I'm not even religious, and I'm certainly not interested in frivolous theories.
I hope you understand that the scientific method carries certain untestable assumptions, e.g. we live in a positivistic universe, that have been proven false for literally thousands of years.
Let me ask you this: If you have a set of empirical data that appears a certain way, but a logical or mathematical proof indicates that your interpretation of the data is flawed, would you dismiss the proof because it is non-empirical?
The introduction of philosophy may render a theory unscientific, but in no way does it imply it is worse. The scientific method is *not* the highest standard for knowledge as it owes an extremely large debt to philosophy and mathematics.
I am not saying you are religious, just that the way you are describing this sounds religious rather than scientific.
I'll try to answer: If I have a set of empirical data which I interpret a certain way, and a logical or mathematical proof indicates that my interpretation is flawed, I would not dismiss the proof I would examine the analysis and try to find a new analysis which fits both the empirical evidence and the mathematical proof. Thus is the scientific method: generate empirical evidence, check to see if it agrees with the theory, if they do not agree then you adjust the theory.