Rarely do I get a response to a post that I so completely agree with. There are several aspects of your post that I would like to expand on. Usually one copies over and replies to each paragraph for completeness. But I prefer to wing it.
First of all with regard to intelligent design: it seems to me, following your ideas of the natural and supernatural, that the mechanism, or at least one aspect of it, for intelligent design is staring them in the face. That mechanism, the mechanism used by God if you wish, is self-organization. God as you say must act through nature and not from the outside of it. Several threads of thought emerge from this claim:
1. Proofs of the existence of God, as intelligent design seems designed to be, will forever be ambiguous. One cannot say if nature is acting independent of God, or if God is influencing nature, or if God is nature.
2. A second thought is that to me it seems more likely that self-organization, while not as random as the mutation process, is more random than the selection process. That is, the number of new designs produced by self-organization probably vastly exceed the number that could survive the selection process. So most of them must fail, just as almost all mutations must fail. And following this thought, it seems to me that God can most efficiently intervene in the selection process; and the mechanism of intervention would be coincidence. My life appears to be run by a series of coincidences. So I would expect the same on a molecular and cellular level. On the other hand, we do not know the laws of biological self-organization. Maybe the number of possible designs are limited. But I do expect it will be more like the gene pool with a large number of possibilities to be selected from.
3. The whole idea of supernatural intrigues me. Superfluids of known properties are known to exist near absolute zero. All the particles are entangled producing quantum coherence on the macroscale and resulting in a lack of friction. I believe that the supernatural medium discussed in religions and in the occult is an actual superfluid composed of particles that are so light in mass that their wavefunctions overlap on at least a global scale; and furthermore that we detect this supernatural medium indirectly, as it makes up over 99% of the mass of the universe...and is called Dark Matter.
So as in #1 above, I can never prove that Dark Matter is heaven. But I can choose to believe that it is so, just as I can choose to believe that God and possibly, even more likely, gods exist. But to reinforce free will to make this choice, God or nature will always be too ambiguous for any proof. However, human experience, like my series of coincidences, or direct cosmic channeling, which I have also experienced, will foster a rational belief in the supernatural and/or God. I tend to think of God as an aspect of the supernatural that is collectively intelligent. It could be self-organization of the supernatural.
4. Self-organization is as far as I know a completely mathematical thing. It is seen in computer experiments, but I am not sure it is seen in nature. Black holes are a form of self-organization, except that the threshold is in mass rather than complexity. And even black holes can only be observed by inference.
The existence of a threshold in complexity reminds me of the Incompleteness Theorem. My belief is that a form of mathematical communication occurs between math systems and subsummed math systems when the threshold is exceeded. Sheldrakes 100th monkey story, if true, would be a biological manisfestation of this process. In this case the supernatural subsummes the natural.
If true, that form of communication could possibly influence self-organization, and would complete the mechanisms by which the supernatural could achieve intelligent design. We should write a book on the mechanisms of intelligent design. The religuous right would make it a best seller.
5. So God is a mathematician. I think the sums up the end remarks of your post. I have not read your links yet- but will shortly. I have always preferred to think of God as a physicist. But I have to agree with you based on the degree to which nature seems to be mathematical, seemingly hiding the fundamental laws of nature in an abundance of the highest math, thereby preserving our inability to prove the existence of God.
Pleased to discuss this with you,