Hello again Richard,
It's good to see we share so much of our view in common. Although, I would like to clarify my position with respect to self-organization:
"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."
To use Pi as an example again, imagine if a formula to compute Pi is similar to an algorithm in nature that produces a self-organized system. In the case of the Pi algorithm, the numbers will be random for all apparent purposes to the observer. Similarly, the self-organized system will be also be apparently random.
Now, let's say that in the case of Pi, the person doing the calculation of Pi is given a dollar everytime there are 5 one's in a row. Perhaps such a sequence happens every few million digits, and the person gradually accumulates dollars. In the case of self-organization, let's say that a species lives a million years or so every few hundred million attempts at introducing new DNA into a species gene pool.
So far, perhaps we are in agreement to your point in #2. But, now we come to the Miraculous Bailey-Borwein-Plouffe Pi Algorithm and Euler equation involving Pi. In the case of the BBP algorithm, we find that all those digits weren't random at all. They were all part of a predetermined sequence that 'exists' and allows person doing the Pi calculation to use the BBP algorithm to jump ahead of their calculation to the trillionth digit if they so wish to do so. Similarly, I believe, all of the supposed haphazard behavior of evolutionary processes that led to deadends and all sorts of other 'failures' in evolution, all are seen in context of the some predestined occurrence. Failed events in evolution are just as predetermined as those events of wonderous design which many religionists believe give meaning to the world.
Taking it further still, we look at Euler's equation that brings a simple and beautiful relationship between the basic constants of mathematics, and we see that Pi (i.e., the long numerical result of a specific algorithm) is all part of a particular beauty of things. Pi makes perfect sense as part of the whole in mathematics. So likewise, I believe, the evolution of the universe in the haphazard manner that we see, is also part of a greater whole of a divine plot.
God is a mathematician, but I think more to the truth, is that mathematics is simply an outcome of God's Being. God is, therefore the Whole (which includes mathematics) is all in conformance to his very Being. It just so happens, as a matter of brute fact, that nature is organized along these principles, and therefore must obey God's will (or God's act of Being) and as a result of that fact, it must proceed along the path very similar to that of Pi - of apparent randomness.