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Of or relating to existence outside the natural world.
Attributed to a power that seems to violate or go beyond natural forces.
Of or relating to a deity.
Of or relating to the immediate exercise of divine power; miraculous.
Of or relating to the miraculous.

That's a dictionary definition, and it does not say a thing about "outside of our ability to observe, test, and replicate." It may imply as much, but scince science is "agnostic," it cannot be ruled out. Maybe we can't observe it now. That doesn't mean we never can or will.

Intelligent design is not by definition "supernatural." Intelligent design is well within the grasp of science and in fact exemplifies what science is about. The first hypothesis could not be made without intelligent design. It is not unreasonable or unscientific to attribute predictable processes to the result of intelligent design.

You'll have the strain the meaning of science beyond usefulness or reject large portions of evolutionist thinking if you honestly think intelligent design is unworthy of scientific merit and subject to pure speculation about the "supernatural."

The evidence for intelligent design is largely, if not completely, circumstantial, inferential evidence. That does not make it "unscientific."

"That's a dictionary definition, and it does not say a thing about "outside of our ability to observe, test, and replicate."

But all of those examples you gave ARE outside our ability to observe, test, and replicate. And what about the FIRST example you gave?

"Attributed to a power that seems to violate or go beyond natural forces. "

If something violates or goes beyond natural forces, there is no way to test it. It is by definition outside of science.

"Of or relating to the immediate exercise of divine power; miraculous.
Of or relating to the miraculous. "

If something is a miracle, it is by definition outside of natural processes and is therefore outside of the province of science.

"Intelligent design is not by definition "supernatural."

Yes it is, it postulates causes which have not and CAN not be observed. That's considered one of it's virtues by ID'ers.

"The evidence for intelligent design is largely, if not completely, circumstantial, inferential evidence. That does not make it "unscientific."

It is entirely nonexistent.