Thomas,
I don't know if you've had a chance to check out Joy Christian's article here. It claims that all of the so-called violations of Bell's inequality are based on an erroneous calculation. If so, the current interpretations of non-locality and non-reality are incorrect. I believe this to be the case, but only time will tell.
You quote Weyl to the effect that: "objectivity means invariance with respect to a group of automorphisms."
I would see this world as a perpetual motion machine, 'auto-morphing' endlessly into itself in meaningless fashion. Definitely compatible with nikman's "In it there is no value...". There clearly would be no room for either free will or randomness, but I see that you covered this at the end with "chaos", although it's unclear how order and chaos are coupled into one reality.
It is also unclear to me how 'scale' plays into a purely mathematical world, but perhaps it can.
I also wonder, from a theoretical viewpoint how one can reconcile such a reality with different coordinate systems. I have worked in Cartesian, spherical, cylindrical and other systems, but one of my physics books describes eleven different coordinate systems used in physics. Let us consider any problem, say the hydrogen atom, solved in each of these coordinate systems. Surely we will not obtain the exact same answer for all of these systems, so which one is "right"? If the universe is only mathematical, one of them must surely describe "reality".
There seem to me to be other problems in this perspective, but I'm curious as to your response to the above.
Finally, you state:
"Reality in its totality, then, encompasses both the cosmos(order) and its complement(chaos)."
This dualism appears to me schizophrenic, with an unbridgeable gap between the order and chaos of our universe. At this point it becomes meta-physics, not physics.
No one has any special authority to criticize anothers meta-physics, but we do have a right to our own preferences, and my preference for decades has been a unitary metaphysics that I believe is best represented by an objective substantial reality that connects order and chaos into one whole universe.
My brief introduction to this approach is here.
Edwin Eugene Klingman