A couple things I've noticed, Tremendoustie:
You've begun inserting several comments about how things should or ought to be, and including as your criteria for belief requirements that a belief be useful to living. These things are scientifically irrelevant. These positions inherently bias any knowledge towards the human or personal perspective. If the truth is one's goal these things have to be set aside. If the truth of the workings of the universe leave human beings feeling helpless and meaningless it is no less the truth, and it is no less important to know.
I certainly agree that evidence must be considered first. When there are two models which both fit the evidence, however, I do think it's worth considering which theory is the more useful. To use a well worn (but I think illustrative) example, the evidence does not contradict the idea that the physical doesn't exist at all, and I am only imagining everything I perceive. It's certainly possible. Yet, the theory isn't really useful -- it leaves us at a dead end. If there are two models which both fit the evidence, I think it is reasonable to choose the one which is most useful. I agree, however, that one should not accept a model which does not fit the evidence, just because it is useful.
Also, I think your definition of supernatural has some weaknesses. You bring up the subject of gravity, suggesting that it is a scientific/physical phenomenon. Let's look at the characteristics of gravity. It is a force which can not be seen, smelt, touched, heard or detected by any other of our senses. Only it's affects can be seen. There is no physical connection between masses which draw them together which we have yet to discern, although some theorize the existence of gravitons. The atomic and subatomic forces working upon neutrons and protons are a very similar case. We can only detect them by their affects. Yet you do not posit that these are supernatural phenomena.
Let's compare that to self-awareness. It can not be seen, smelt, tasted, touched, or heard but we can observe it's affects. In fact, self-awareness is even more a physical phenomenon than the two prior examples since we can affect it through physical manipulation via chemicals, electromagnetics, or even structural alteration of the brain.
How then is self-awareness supernatural and gravity is not?
Great thoughts! Actually, I'd rather ditch the word supernatural entirely, and focus on the physical or non-physical, if you agree. I think it would be more precise, and less loaded. So, where I say "non-physical" you can think "supernatural" if you like.
First, let me address your question about definitions: I would say gravity is a physical behavior simply because it describes the behavior of matter. Certainly gravity could have a non-physical cause (perhaps a god chooses to apply the law of gravity). But, it is not a non-physical behavior -- a non physical behavior would describe the behavior of something non-physical.
Self awareness is different, because it's definition is not the behavior of matter. Gravity describes the physical behavior of matter. Self-awareness describes the perception of a mind. It is not literally a description of the behavior of matter -- so it is not a physical attribute, but rather, a non-physical one.
You bring up an important point, which people often forget. Science doesn't really explain how or why anything happens -- it just forms rules describing how things tend to behave. At best it can show how two seemingly distinct behaviors could really be based on the same rule (e.g. an apple falling could really be the same rule for behavior as a planet circling the sun). This is the reason I say that physical observations can never prove the non-physical. If a physical behavior occurs too rarely to be repeatedly measured, it is considered an aberration, or due to observer error. If it occurs sometimes, it is considered random. And, if it occurs all the time, it is considered a physical rule. Science will always adjust to any physical observations that are made -- there is no physical behavior that cannot be explained based on some set of physical rules, combined with some randomness.
There certainly seem to be deterministic rules which matter tends to obey. There also seem to be some random effects (or theoretically unobservable variables, which is the same thing). This is the extent of what we can know based only on physical observations.
Now, by self-examination, I think we observe that the mind exists. We can be quite confident that matter can affect the mind, as you have pointed out. The question is, is the mind also a third cause, or is it only "along for the ride", and unable to cause anything itself?
I think the most reasonable model is that the mind can in fact affect the physical universe. This is certainly what we perceive, and there is no reason to disbelieve it. Yes, perhaps it is possible that the perception that we have the power to make decisions is only an illusion foisted upon our consciousnesses. It's also possible, as we have noted, that physical reality itself is an illusion created by our own consciousness. However, when two ideas fit the facts equally well, I think the most straightforward, least elaborate one is the most reasonable. That is, I think an elaborate deception is an unnecessary device which the facts do not justify.
I think the model that both the physical and non-physical exist, as well as deterministic, random, and intentional causes, is the most straightforward, and matches the evidence as well or better than any other. It is also the most useful, I think, allowing the greatest scope for exploration, and not having the ultimate logical conclusion of insanity.