Bear in mind that you are building this argument on assumptions about the truth of natural selection and the possibility or probability of other explanations existing.
You can't formulate any mathematical rule that distinguishes a produc of selection from a product of some other cause.
I think you are missing the point. The only thing a mathematical formula will tell you about a pile of 1,000 face up nickels is the odds of 1,000 nickles randomly falling into a pile face up. It will not tell you whether the nickels randomly fell there or were placed there. Given no certainty, you need to make a judgement call about what you think the most likely explanation for those 1,000 face up nickels is. Do you think they were placed there on purpose or fell there randomly? You could make the case either way. And what's important here is that it can be reasonable to make a judgement call either way in the face of unknown or unknowable factors. You guess based on the preponderance of evidence and probability, not simply possibility. Other people might guess differently. But it's still just a guess and it doesn't mean that the question doesn't exist or that one perspective or the other is invalid. It just means that two people look at the same evidence and consider different things to be the most likely explanation.
You seem to want certainly. As Dimensio pointed out, "Nothing in science is ever 'proven beyond a shadow of reasonable doubt'." If that's true, then why are you demanding a level of evidence and certainty to prove intelligent design that the theories of natural selection and evolution that you support can not even achieve?
the biggest problem for ID is that we can see selection at work in real time. ID does not bring any ongoing process to the table.
Why is this relevant? Plenty of scientific theories about how things originated and formed (from the origins of life in a primordial soup to the formation of our moon and solar system) are not necessarily observable as ongoing processes. The absence of an ongoing process does not preclude the possibility of looking for evidence of processes that happened in the past but are no longer happening. What you really need to do is think about these demands you keep making and questions you keep asking in the context of other branches of science. Are they really requirements for a theory to be reasonable or are you simply demanding that any competing theories about the origins and development of life share the characteristics of evolution because that's the incumbant theory?
I am not assuming the coins were placed there or occurred randomly. I am saying they were placed ther by a process that we can observe, model mathematically, emulate on a computer, and which is sufficient.
It's your turn to produce an agency whose properties can be observed, described and modeled, and which is sufficient.