A supernatural explanation in itself is a huge assumption.

First, you have to assume that a supernatural being exists, then you have to assume that that supernatural being interacts withthe physical world.

No, it's fine.  If you're having trouble PM'ing, I'll do it out here.  No personal worries, either.

In any event,

I'll explain my statement of things not being able to create themselves (not that it matters to much since you're rolling with it, but I might as well): To say "This thing created itself" would imply that it existed before it existed (otherwise, how could it create itself unless it was around to create?), which is nonsense.

Now, I will clear this part up here and now: the second observation in the scenario is not a counter-observation.  A counter one (or, contradictory, whatever suits your fancy) would be "Matter can be created physically"  My 2nd observation does not have "physicall" in it, so it is not contradicting it.

As for how, then, I get anything out of it,

"So, then, how do I get the supernatural out of it if they don't actually contradict? By this: given that my 2^nd observation involves the creation of matter, it follows that it had a means of creation (things cannot create themselves; that's illogical). And, since we've already established that things cannot physically be created, we are left with only 1 option: a non-physical creation. If the objection is raised that “Science is not supposed to conclude on the supernatural”, what then do we do? We cannot conclude that our 1^st assumption is in error, because we do not have any counter-observations at hand (otherwise, that basic tenet of “If observed enough, it is assumed true” is contradicted), unlike my previous paragraph. You could say “well, I guess science has failed this time”, what does that actually mean? That doesn't solve the contradiction. No, the only thing left (I posit) is to throw away the objection that science cannot conclude on the supernatural."

In light of my explanation of how the two observations interact, I repost this, hopefully having given the clarity lacking from my example, for it lays out my case for the deduction of the supernatural.

"BUT WE'LL NEVER KNOW THAT unless you can somehow prove that no natural explanation can possibly exist." 

Fully agreed.  As you note, my 2nd example moves towards that (my first one does at well, but it probably was not very clearly worded, so that may have been missed).

"The problem is that, not being gods, we cannot be sure that we have actually exhausted every possibility, every hypothesis, and every idea without mathematical proof, so instead of 'no physical cause' it should be 'no KNOWN cause'"

This is indeed true.  On the other hand, it's true of all science; every last bit of whatever conclusion science comes to is inductive (of course, not that I think there are methods of proof at all, as you well know :P  ).   So, to say suddenly "Ah, but that's inductive!" is to blow the whistle on all of science's conclusions, and undo any assumption you have ever made using science.  We have, many times, agreed that science makes assumptions on these observations.  So, in the event of my example, science would, just as it does anytime else, assume that what it has observed is indeed the case.

In the event you (or anyone else, for that matter) decides to drop the idea that science does make assumptions, but merely says "Ok, if observed enough, it is likely true".  Well, then, it is likely that there is a supernatural (note that this is just as much a statement of science as any other).  This does not need to be tested for, because you've already tested it.  For example, consider the following,

"I was hit by something.  It was, likely, not a car.  Therefore, it was, likely, a non-car"  Saying "That which hit you is not a car" is logically equivalent to saying "That which hit you is a non-car".  It follows quite nicely (I posit).

While that may be true, my scenario is a hypothetical one, one in which quantum mechanics is either impossible or unobserved.  I'm aiming to demonstrate the possibility of a supernatural explanation.

For the first (non-issue) item, why are you ruling out something happening without cause?  

(Insert segue here)
Your first statement was "that matter cannot be created physically...", and the second was "...that matter comes into existence".  Now, taking "physically" literally (either definition) this makes no sense.  Firstly, because no such observation has been made, and in fact physics allows for the creation of matter given enough energy being spent to that end.  

And when I read it the first few times, I thought it was the  meaning of physically as in "I am physically in Best Buy" (as opposed, perhaps, to their online store), and so those two statements would be contradictory if matter was created in the "physical" universe.  

Now, as for the other meaning I can think of, as in "in accordance with the (currently known) laws of physics", that is only a contradiction of the laws of physics, and not science or nature as a whole, so perhaps that is what you meant.  

Only then you turn around and say that "non-physical cause" = "supernatural cause"!  ("we are left with only 1 option: a non-physical creation")  This, of course, would massively fail to support your point given the latter definition of "physical".  

It would be senseless for me to pursue this any further until you resolve the above.  

Also, I ask for consistency in another area:  you claim "deduction" of the supernatural, and then (it seems) explicitly use induction to get there.   

P.S.  What about the "exports from another universe" hypothesis?  How could we eliminate that possibility, as we must for even your idea of science to contemplate the supernatural?   

"P.S.  What about the "exports from another universe" hypothesis?  How could we eliminate that possibility, as we must for even your idea of science to contemplate the supernatural?"

We have detected no physical cause: if it were exported from another universe, and we found no trace of a physical transportation.  Then, science does what it always does; assumes that there is no means of physical transportation.  That doesn't rule out another universe, mind you, but it does mean that there was a means of non-physical transportation, so the supernatural as an explanation is present either way.

More simply, we could just pretend that, in this scenario, multiple universes have been mathematically ruled out.

Nice try, but although I think we all know what appolose is trying to get his foot in the door for, his argument does not involve any specific entity.

For this non-issue, I would say that it is illogical to say something can be without cause.  For one, it can't create itself (as I noted above), and, for another, to say "It came into being without cause"  again implies existence before existence ("It came"?).  Also, no, quantum mechanics does not contradict this (a quantum flux is responsible for matter creation, not "nothing")

As for observing the inability to physically create matter; such an observation already has been made (possibly that's now overturned due to quantum mechanics, but this is a hypothetical situation, remember?).  In fact, it's the first law of thermodynamics (let's not confuse that with being contradicted by E=mc^2; it isn't (not that that is relevant right now)).  As I said before, once science observes something enough (in this case, the absence of a physical instigator) it assumes it's true (or says it's likely, for anyone who wants to change what we agreed science does).

"And when I read it the first few times, I thought it was the  meaning of physically as in "I am physically in Best Buy" (as opposed, perhaps, to their online store), and so those two statements would be contradictory if matter was created in the "physical" universe".

While I'm not sure if I'm understanding you here correctly, I offer this: To be created "in" does not imply to be created "by", if that answers your question.

"Only then you turn around and say that "non-physical cause" = "supernatural cause"!  ("we are left with only 1 option: a non-physical creation")  This, of course, would massively fail to support your point given the latter definition of "physical"".

I'm not sure of what you're getting at here, actually.  What definition of physical are you referring to?  My only goal here is to demonstrate that science can reach beyond the physical as an explanation, which would be, therefore, non-phsyical, which I am calling supernatural (It makes no difference if you want to haggle over the meaning of the word "supernatural"; that isn't the core point here and never was).

"Also, I ask for consistency in another area:  you claim "deduction" of the supernatural, and then (it seems) explicitly use induction to get there".

Deduction from the assumptions of science; you can make a deduction off of any two propositions, regardless of the truth value of them.

"P.S.  What about the "exports from another universe" hypothesis?  How could we eliminate that possibility, as we must for even your idea of science to contemplate the supernatural?"

We have detected no physical cause: if it were exported from another universe, and we found no trace of a physical transportation.  Then, science does what it always does; assumes that there is no means of physical transportation.  That doesn't rule out another universe, mind you, but it does mean that there was a means of non-physical transportation, so the supernatural as an explanation is present either way.

More simply, we could just pretend that, in this scenario, multiple universes have been mathematically ruled out.