I think it would help if you knew what the cable did to the signal, in technical terms. If you could measure that, it may be possible to derive a test signal that accentuates the difference. I know this won’t tell you if you actually like the sound better or not on real music, but it will allow you to determine at least that you can actually hear a difference. I know they can do this for absolute polarity. A properly made test signal will make the difference quickly apparent for most listeners, while with regular music it can be very difficult for most of us to tell. It’s a nice thing that our hearing is generally quite forgiving of small differences. I call it subconscious auto correct.
I’ll now offer an anecdotal tale. I had a customer measure the clarity of his bass after he made some adjustments to his room and system. I analyzed a bunch of his measurements and they all were very good, with one setup being slightly better than the rest. He then told me that a DIY power cord he’d made for his subwoofers seemed to improve clarity, so I asked him to make comparison measurements with and without the new power cord. Guess what? The clarity measured higher! Now it could be just a random result. We’d have to control all factors very carefully to be sure the change was a result of the power cord. But it does suggest that measurements can demonstrate these differences if someone is willing to take them.