Exactly by just plugging in the cable and listen, what simpler physical experiment is there?
That's a simple enough experiment, however your "measurements" there are massively unreliable. I have "seen" things that weren't there simply because my mind fills in the gaps, such as the blind spot. We all know that there is a blind spot in each of our eyes. That's an inescapable science fact. But why can't we see it? Because the mind fills in the gaps and has a guess at what's there. Same as the fact that we see double, but our brains correct it. If you're going to observe someting you have to be able to demonstrate that your observations are reliable. Mine aren't I know. You think that yours are? Hmm. If you like.
Or you mean a publication in Nature?
If you want, or any other repeatable, reproducible experiment.
My point is that if you want to say "I have had a listen and I think it sounds better with X or Y, that's an end of it" then that's OK. That's a faith based argument. It's like saying that you are a Christian and you see evidence of God's work everywhere you go. If that's your belief, fine. I don't believe in God, I don't believe that mains cables make the audible differences you describe, I think God and your audible differences such as noise reduction mains cables work well on sources but not amplifiers are imaginary.
However you haven't said this, you are talking about shielding reducing noise (OK, maybe, so demonstrate it) and LCR differences (again, show me. It's easy, known science.) Electronic engineers know how transistor amps work, this is known for 60 years, it's mature technology to the point where 50 year old circuits (the Hitachi MOSFET, the RCA. etc) are still in use, with modifications, and yet we are to believe that there is some unknown science happening in the 2M of cable between the wall and the socket in the back. What's that then? Why doesn't it happen elsewhere? Why is it only happening in consumer electronics and medical or scientific instruments don't show it? Aren't they precise enough?