Main Question: Is the concept of Artificial Selection just a convenient terminology, or is it considered scientifically differentiated from Natural Selection?
There's basically two ways to dichotomize the word "natural".
One is the natural vs. supernatural dichotomy.
Another is the natural vs. artificial dichotomy.
For the natural vs. artificial dichotomy, artificial means "man-made" while natural means that it was not man-made.
So, when a selective pressure is referred to as artificial, that just means that it was caused by man.
There's really nothing more to it than that. Its just a distinction that we've created for our own purposes.
I am not able to grasp why human intention is considered to transcend natural process, at least when speaking scientifically.
Human intention is still a natural process, in the sense that its not supernatural, but we do separate it from processes that we have no hand in because, well, because we're the ones making the rules and that's how we want to do it.
Is there some massive miss-step that I am making with this line of reason?
I think you're applying more to the distinction than is intended.
Say you found an a sharp triangular stone in the dirt, like an arrow head. As a geologist, you may be interested in determining if unintelligent geological processes could have formed it, or if it was made by a person on purpose. To distinguish between those options, you may refer to the first as a natural process and the second as an artificial process. But calling it an artifact only means that it was made by man, not that it was some supernatural process.
Or we could look at something like the banana. Regular old naturally occurring bananas are full of seed and have very little fruit. The bananas at the grocery store are the result of a long line of man-made selective pressure (and cloning).
The purpose of referring to that as artificially selected is just to distinguish is from the process that occur in nature without our help. There's really nothing more to it than that.