I think all your 'quibbles' are important, giving me a chance to focus on some of our key issues.
"One quibble with your essay was with regards to the claim about the mystical nature of many great mathematicians and physicists. My sense of being a mystic is that it mostly entails a sustained inward commitment or awareness, and that tends to place the intellect in the backseat."
The historical fact is that essentially all those great people who deserve to be called 'fathers of physics' were mystics. This is true not only for Pythagoras and Plato, but also for Galileo, Kepler, Descartes, Leibniz, Newton, Euler, Gauss, Faraday, Maxwell, Planck, Einstein, Schrodinger, Heisenberg, Pauli, older Dirac, Wigner... You may read about that, for instance, in a wonderful recent historical treatise of Wagner and Briggs, "The Penultimate Curiosity", or enjoy "Quantum Questions: Mystical Writings of the World's Great Physicists", collected by Ken Wilber, or in "The Music of Pythagoras" by Kitty Ferguson, to name just a few.
"You talk a lot about the significance of intellectual beauty. On the hand I suggest that a lot of progress (intellectual/spiritual/whatever) is derived from the obstacles and suffering we encounter. "
The high importance of the intellectual beauty is not my arbitrary claim; I am finding that in writings of those highest rank mathematicians and physicists who cared to express their worldview. Moreover, I think everybody with sufficient mathematical experience knows that in his/her heart. Mathematics is loved by many people, and it is loved for its beauty. Obstacles and suffering may play an important role in ways that beauty is revealed to us, as, for example, one may read in the book of Job.
"I think that the underlying reality is that religions were on to something real and science should be open to that possibility."
I do not think that science, as a special mode of cognition, can be open to religious reality. Science is limited by its strict exclusion of all subjective, which makes it so effective. I would rather say that scientists should not be as closed to the religious, as science is.
I am not sure that I fully understand your last paragraph. I would say that the God-soul relation is extremely subtle both bottom-up and top-down.
Thanks again for your extensive and thoughtful comments. Stay warm and please do not forget to rate our essay.
Good luck, Alexey.