"If man is natural, then man's intelligence is natural. If intelligence is natural, then "supernatural" intelligence, if it exists, is perfectly natural and remains a viable alternative explanation so long as any question remains."
You've only shown that man's intelligence is natural, not all intelligence. This means that supernatural intelligence may not necessarily be natural and your argument falls apart. You still need to show that supernatural intelligence is natural. This will be difficult because of the definition of 'supernatural' which means, I believe, above nature. It appears that anything supernatural is not natural by definition.
I'm not sure that one can draw such a clear distinction between "natural" and "supernatural" as you're trying to do, however. It seems that the distinction only works one way, and that it's largely a matter of perception.
Suppose we created artificial life in a computer. Our position would be in some sense "supernatural" with respect to the universe of that electronic life form, in much the same way that God is "supernatural" to us.
We, however, would see the "computer life" as merely a subset of the larger nature of which we're a part, and God would presumably see us in the same light.
It may be a mistake to assume that the true universe (whatever that is) consists only of those things which we can observe. There are many serious scientists whose work at least raises questions on that score.
Simple. If intelligence is considered natural, then there is nothing above nature and even the so-called supernatural becomes natural, particularly insofar as it interacts with the standard concept of nature, but even in total if you can but access it. Even "God" is natural and operates according to the laws in His domain.