How can we hear the difference in cables in a bad room?

Erik, +1.

It is no different from other sensory fields. You can read a book just fine under the imperceptibly flickering light, as your eye works hard to position for the text you want to read, while the flickering causes it to overshoot and undershoot position, placing extra burden on image processing, and on the extraocular muscles, leading to early fatigue, and for some people, headaches.

To the op, whether one believes cables make a difference or not, what you would be "detecting" is a difference. That does not mean you have made your system good, just different. Better of course does not mean good. I think you can use your own judgment on whether many of the audio adjectives and effects assigned to a particular cable type are viable.

Miller, you may get more traction with your posts if you didn’t start them by extolling your personal perfection while insulting everyone else. To be honest, after this paragraph, I didn’t read anything else in that post:

While the rest are enjoying arguing about why I’m enjoying sounds they can only dream of. Actually maybe not even dream. If their imagination is as stifled as their intellect that would stand to reason.

Extraocular which controls eye positioning. The flickering causes issues with eye positioning.

When reading or similar visual work, you eye uses high speed movements called saccades to change the visual focus point. When reading the movements are small but fast and regular. Most of the body of work on this was done in the 90s, but re-emerged as a topic in the later 2010's as solid state lighting emerged as the next dominant technology. From a paper:

The results are consistent with the view that flicker has two distinct effects on reading, both of which are potentially disruptive. The first relates to an increase in the number of prematurely triggered saccades, which are, as a result, less accurate. The second is an increase in the number of saccades perturbed in flight, which land short of their intended target. These two mechanisms may have different consequences for readers, depending on their reading style.

No, not related to audio, but related to how our perceptive systems can adapt to non ideal circumstances and how even though adapting, the situation is non-ideal, requires addition processing, and leads to fatigue, even though everything seems "okay" on the surface. This was a point argued above w.r.t. brain adoption to room acoustics.