You've been doing pretty well, Richard, on the "healing" discussion, so I haven't interrupted. Instead I'll pick up on a couple of your own points.
Let me address the "sunny wedding", since it is involved with God's "hiddenness". The question of detectability, it seems to me, is based entirely on ones assumptions about what causes weather, ie whether one has embraced that old "Nature hypothesis" upon which I entered the thread.
An anology: one of my relatives is moving next week, and her friend runs his own company, in which (to steal the phrase) he says to one man "Go" and he goeth, and to another "come" and he cometh. In this case (at my relative's request) he's decided to divert a few of his guys and the vans to do the removals, rather than for my relly to pay a removals company.
This is obviously (a) an intervention in response to a request (b) somewhat outside the usual business plan but (c) involves exactly the same vans, the same guys, and the same heavy lifting that he pays them to do every other day. So you could say that to an outside observer, who knows nothing of the management structure of the company, his intervention is "hidden" - but it's hidden in plain sight, because as soon as you realise that he runs the company, you suddenly see that every job is an "intervention". His hand is everywhere to be seen - nothing is, in the end, running itself.
Now his role in ultimate causation is not altered one jot by the question of whether his management style is to run round the office delegating the day's tasks personally, or in most cases to follow a plan (ie via secondary causes) he made in January, delegate admin staff to execute it, and play golf... though the latter gets harder to envisage when a one-off house-move at an individual's request is involved. But he's not hiding, even though he's totally invisible to anyone watching the work being done... phone him up, and he'll speak to you and maybe even do a job for you, if he isn't on the golf course.
Returning to the natural scenario, the fact that one can, to some extent, investigate regular causal chains in the weather doesn't negate the governing will of God, any more than the causal chains within a company negate the overseeing role of the owner. They simply show there is some order in what he plans.
Weather, of course, is notoriously lacking in lawlike order, though. Whatever causes its chaotic variations, the concept of "natural law" is impossible to apply in detail practically, so that it's customary to invoke hypothetical interactions of many laws (which can't actually be tested or even shown to be real as a concept) or concepts like "chance", which is (as we've discussed before) an epistemological gap, not a cause. Meanwhile, meteorologists makes short-term forecasts based on limited regularities and computer models, and what Michael Polanyi calls "personal knowledge", ie human experience.
Even in more controlled situations than weather, though, thinking through the implications shows that the concept of natural law, and even the predictability of the universe, is problematic, as philosophers of science like Nancy Cartwright - no theist, as far as I can tell, have explored in detail. Amongst other things, she reasons that "laws of nature" can make no sense apart from God - one reason she doesn't believe there are laws of nature! Incidentally, she follows most other PoS people in being more careful to distinguish scientific "facts" from "laws" and "theories" than some here.
I've asked [Jon] why isn't there a fossil out of place if God is working in the world beyond its own workings
I missed the context of this, so am not sure exactly what you mean. But the short answer is that, on any scientific understanding, no fossil can actually be out of place. They are regularly found to be so, according to existing knowledge, and since they are a real phenomenon, they are either used to modify the theory ("Mammals evolved far earlier than we thought!"), or treated as anomalies either to be ignored or explained away if they are too far off the current explanatory paradigm (just one controversial example here).
If you're thinking of the overall trajectory of the fossil record, for which there is much clearer evidence than for the exact origins of pretty well any taxon within it**, it's suggestive of common descent, but that tells you nothing to the point of your question except that, under theism, God wanted to do it that way. Or to phrase it another way, the reality that we see (which doesn't include precambrian rabbits, as it happens) tells us not only how we might understand efficient causes scientifically, but equally how we might understand God's creative activity and final causes theologically.
"Working in the world beyond its own workings..." is the phrase I dislike. It implies a belief that the world has its own workings apart from God (and understand here that this has nothing to do with lack of secondary causes, but only autonomous secondary causes). If you believe that, however he does it, nature is what God does, then you see God everywhere, and the wedding weather or the miraculous healing are just special cases of the usual. If you believe Nature to be a system operating apart from God, then of course he's completely hidden, and answers to prayer and miracles become anomalies to be explained away, or ignored agnostically for "lack of verifiable evidence".
"It is the theory that determines what you can observe" - not a quote from a Nancy Cartwright, but from Albert Einstein.
** It's quite a big deal that this year the taxonomy of the entire "dinosaur" tree was completely revised after 100 years.