Dan, your thoughtful and carefully worded essay looks like a search for a way to share a vision or larger idea about the nature of science and reality with the world. You clearly have thought deeply about issues of how our perceptions of reality are fundamentally distinct from that reality, and about how physics and even more so math in abstracting from that reality impose on it our own perceptions and inventions of order.
Your paper has many gems, such as "Evidently nature has its own order consistency, apart from the human need to perceive it. ...[which need is perhaps] why science has taken such refuge in mathematics as the sheer embodiment of reason and order, even as the ontological basis of nature. The alternative is uncertainty and perhaps an inexplicable universe."
You seem very aware of the limitations of science, and how those limitations impact the choice of problems and range of solutions that scientists take up, and the ways this contributes to the illusion that "math applies in unfamiliar domains because ... a parallel mathematical domain is simply there already, waiting for us." Near the end you write "Mathematicians can no longer afford to ignore the genetically inbuilt relation of math to physical reality (the real pre-established harmony) or its significance as a conscious human creation."
Your essay has deepened and fleshed out the question of the contest and laid out a case for the resolution of that question to tilt in a certain direction. What is missing here, although I can see you reaching for it, is a deep and specific explanation of how physics uses mathematics to model the world, how that has shaped mathematics, and why mathematics has been such a troublesome tool and companion.
Please allow me to direct your attention to the contest submissions by David Hestenes ("Modeling the Physical World with Common Sense and Mathematics") on the former and Robert MacDuff ("A Mathematics of Science") on the latter.
Rob's essay in particular addresses the radical idealization embedded in contemporary math - by proposing an alternative system which intrinsically conserves information about the properties of models of observable phenomena, such as grouping properties of quantities, much as Euclid's geometry encodes information about the structures being reasoned about.
This radical departure from the mathematics of the past few centuries opens the way to broadening the range of questions science will have the tools to address. It has had a profound impact on K-12 teachers and their students but has met stubborn resistance from academics of all stripes due I'm sure to the huge investment they have in the paradigm that Rob's work is threatening to overturn.