Thank you for your clarifications; you have made your position much clearer to me, so hopefully I won't accidentally misrepresent it.
"There is one event. The Big Bang."
Well, I would disagree that the BIG Bang would demand the "no natural mechanism" conclusion. At best we don't know enough about what happened during the Planck Era to say which conclusion is best. However, for the time being, we do know enough that I believe the best interim conclusion would be the second of your three choices, the "unknown natural mechanism" conclusion.
"While a majority of scientists (including myself) believe abiogenesis will eventually be empirically explainable via natural mechanisms, a few argue that there are empirically sound reasons for ruling out all known natural mechanisms."
Such people tend to be anti-evolutionists, philosophers who don't understand how science works or non-chemist scientists who don't know enough chemistry to understand abiogenetic mechanisms.
"On the other hand, I believe that 'no known natural mechanisms' is precisely the right conclusion for a variety of singular historical events (e.g. some miracles recorded in scripture)."
That's a good point, but these events are also the kind of things that science cannot study, NOT because they are possibly of supernatural origin, but because they are not reproducible or repeatable, and science can only study what is reproducible and predictable. Now, predictable in the scientific sense does not mean knowing exactly when and where something will occur; instead it means knowing the conditions under which something is likely to occur, including what causes it. For example, we do not no where or when the next earthquake, volcano, tornado or lightning strike will occur, but we know what causes these events, when they are most likely to occur, how they operate, etc.
Similarly, reproducible does not mean on demand in a laboratory, but simply that the event re-occurs often enough that scientists can study it. So while we are as yet unable to trigger earthquakes, volcanoes, tornadoes or lightning strikes at will, they re-occur in nature often enough that we can study them as often as we need to understand them. No miracle could ever be explained scientifically, even if there were dozens of scientists on hand with every piece of equipment imaginable to record and the study the event, because science verifies or refutes the explanation it comes up with by studying the event when it re-occurs to see if the same things happen again. Singular historical events that never re-occur, even if they have perfectly natural causes, cannot be explained scientifically. Assuming they leave no evidence of their occurrence, that is.
"That is why I think the 'no known natural mechanisms' hypothesis is worth stating explicitly."
But at what point in the research process do you say, "I can't find a natural mechanism, so I will conclude that this phenomenon cannot be explained by natural mechanisms", especially if all you have is negative evidence? Put another way, what kind of positive evidence could there be that would convince you that you must conclude that no natural mechanism is possible?
Kevin L. O'Brien