The proposal of any sort of deity is constricted by the fact of it's total lack of necessity.
You can always come up with more than one explanation. Creationists are doing it all the time. The question is, which explanation sounds more likely, and which explanation sounds like an attempt to explain away inconvenient facts. If you think that creationists have got a monopoly on the latter, you are wrong.
Every proposal of god that has been able to be tested has revealed a natural cause
Not so. There have been postulated natural causes, some provable, some not.
and that there is no good reason to hold such a belief as the supernatural,
Like I said, it comes down to a subjective judgment about which of the proferred explanations sounds more likely.
thus leaving the argument with three types of arguments, one's that we know are false, ones we cannot test at this point in time and ones that we can probably never test.
It sounds as if you have already made up your mind.
If you believe in such an entity, then something has convinced you, as belief is the result of being convinced, what causes YOU to believe.
I believe for all sorts of reasons, but if I was trying to get somebody as far as Deism, I would probably point to somebody like the following astrophysicist, and professed atheist. Whether he ever formally abandoned his atheism, I don't know, but he certainly sounds as if he should have done:
"Would you not say to yourself, 'Some super- calculating intellect must have designed the properties of the carbon atom, otherwise the chance of my finding such an atom through the blind forces of nature would be utterly minuscule.' Of course you would . . .. A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question." (Fred Hoyle)
The book I posted a link to could expand upon that. But for example, if gravity was one part in 10 to the fifteenth stronger than it is, then it would have collapsed back in on itself shortly after the big bang. On the other hand, if it was weaker by a similarly miniscule amount, the stars would never have formed, and there would be no elements hevier than hydrogen and helium. The latter is inert, and the former would have nothing to react with. Astrophysics is full of "lucky" conincidences, and the universe appears to be balanced upon a knife edge. So is there a designer twiddling the knobs, as one physicist put it, or are there billions upon billions of other universes, unobserved and unobservable, and we live in the one which just happened to strike lucky in a cosmic lottery? And which explanation sounds the more extravagent?