Just trying to light off some fireworks here! :^)
Truly, you've touched on every aspect of the debate. I look forward to the comments to see where the interests might be. For now, I only have two points to raise.
First is qualia - love, hate, joy, pain and so on - which can be experienced but not conveyed. A computer cannot be programmed to experience qualia. It is a phenomenon of autonomy in nature that has no materialistic explanation and thus the naturalist's defense is to deny qualia exists in the first place.
Second is the term "random" which as you have pointed out is inappropriate to use with reference to a system when one does not know what the system "is." Since the number and types of dimensions are both unknown and unknowable, it is inappropriate to say a phenomenon is random in nature. The proper term is "unpredictable."
The word "unpredictable" does not preclude as yet unknown causation and can be applied without reference to what the system "is."
Sadly, the term "random" has been misused in science for so long it would be difficult to correct. Nevertheless as we discussed on another thread recently, ideologues must not control the dictionary.