Can we agree that there are qualities to music reproduction than can not be scientifically measured?
There is no need to agree or disagree on that when it can be determined by listening tests. In fact, worrying over such matters can be a distraction, a potential source of bias, while doing these tests. If you agree, then why try to test it when you already believe it cannot be scientifically measured. If you disagree, because you can't accept the idea that a simple wire could possibly make a difference, then why bother with the test? To do a fair listening test, you have to agree to suspend your belief or disbelief, and accept the test results.
If we can, then I am interested in auditioning in a blind test the same song with two different cables. Waiting for a repaired silver headphone cable which I will compare to a stock Audeze cable....and a new DHLabs cable to replace an ancient Monster cable. Should be able to post results next week. I am pretty sure I will be able to tell the silver headphone cables 5 out of 5 times. I noticed difference and preferred immediately (no "break in" haha!)
When you run the test be certain to include negative and positive controls.
The basic test, if I understand your intentions, will involve you listening to your headphones while someone else, not you, switches the headphone cables. You must not know which cable is in use.
The negative control is easy, listen to headphones while someone else, not you, goes through a mock cable switch. Instead of listening to cable A vs. cable B, you will be comparing A to A, or B to B. How many times do you hear a difference under those conditions? It won't be zero. You must then subtract that negative control value from that of the A vs. B test.
For example (I'm just making up some numbers here to make it easy to talk about it) let's say the real test shows you can hear differences between A and B 75% of the time, and the negative control test shows that you hear differences between A and a or B and B 25% of the time. 75% minus 25% = 50%. That wouldn't be bad. However if the real test resulted in 50% and the negative control was 50%, subtracting would get you 0%.
A good positive control test is more difficult. I'll postpone discussing that for the time being. However, if you do get positive results, a suitable positive control becomes necessary to make your results believable.
Statistics are also necessary. If you end up with a positive percentage after subtracting the negative control, you have to deal with what statisticians call confidence levels. Typically, they like to see confidence levels of at least 95%. That means the if you repeat the test 20 times, you would expect to be correct 19 times. You may not like hearing that, but a 95% confidence level is the minimum. It's not setting the bar too high.
My point is that doing a convincing listening test is not so simple as doing 5 trials when a friend switches the cables while you don't know what cable he chooses.