Doug, I like you "metaphor" of the path integral. It is good that you manged to get some real physics into your essay as we are supposed to. I am sure you know that when Dirac first though of a path integral in physics he saw it is more of a metaphor than a real theory. Feynman realized that it really works and is not just a metaphor. perhaps the same is true of your idea here.
I appreciate the idea that it is not just the classical path that counts. We need some thinking away from the mainstream to contribute its part. It is just a case of getting the right Lagrangian so that everything has the right weight and leads to the correct unbiased answer. I think some AI technology will use this kind of technique to get the right conclusions from the sum of human thinking and help steer humanity