I rated the message 4, I assume this is what I am supposed to do, while I type my response?
-- I pretty much agree with your definitions. I think science is the attempt to explain things,
naturally.
There is a whole area of semantics here that people get confused about.
For example, is something "unknown", natural? If we now know it, does it become natural? For example, if you observed, experimentally, the Red Sea parting, does such phenomena become natural?
Also, we forget how mundane the universe is to us. We are NOT usual. If I knocked on your door, it wouldn't amaze you much. But if ET knocked on your door, that would amaze you!
Why? Because you have never seen ET? or perhaps, you have never understood how amazing animated matter actually is. (I speak hypothetically).
My point is - we could also ask; what is miraculous? Are natural things miraculous?
If the universe was created, then every "natural" law etc... all become supernatural/miraculous, perhaps.
The biblical understanding, is that the physical/natural manifestation, only comes because of a spiritual cause.
Just some of my thoughts, I am not trying to prove anything.