OTLs are an excellent example as they will have a totally colored response compared to probably virtually any other amplifier type with any given speaker. You can choose one that works best, but no matter what you do, it will sound different with other speakers. A quick review of your posts shows you pairing it with speakers that were not intended to be used as such.
Your interpretation of how the ear perceives harmonics is too simplistic to be useful as a rule. Here is a link to help: https://www.researchgate.net/publication/323914860_THE_EFFECTS_OF_DISTORTION_ON_THE_PERCEPTION_OF_LOUDNESS_IN_LIVE_SOUND Low feedback will result in mainly compressive distortion. Insufficient feedback will result in expansive distortion using their defined parlance.
W.r.t being easy to demonstrate with simple equipment, I agree. I low distortion amp, low distortion amplifier (across 20KHz), and low distortion headphones. Then use a distortion simulation program like Distorter (VST plug in) to simulate various level (and orders) of distortion, or Pkanes Distort. Sure if you did 0.1% distortion of purely higher order for a 500Hz tone, you will hear it before lower order distortion but you and I know that is not a realistic occurrence. And this is detecting with a pure sine tone at optimal frequencies. With real music, no way.
Take a perfectly digital source and low distortion SS amp. Then add in the distortion profile of a typical SET amp especially the 2nd/3rd distortion, at levels one could expect outside clipping. Then blind A/B them with music. It won’t sound warm or cold. On general music you will notice the distortion before you notice any warming ... and yes, I encourage everyone to repeat this experiment themselves if they have a low distortion DAC/AMP and preferably headphones as lower distortion but you could use speakers. Please don’t take my word for it. That whole "warming" due to typical distortion components of tubes is just Philelore.
Yes the brain does have a variety of tipping points, but it also has the ability to extract the underlying information out till things get really bad. It will not pay attention to this distortion tonality more than it will the raw frequency response.
So where should I be looking for this connection between measurements and audibility? Feel free to send a link with some sort of objective listening test of distortion (and reasonable levels) versus tonality, where the only variable changed is distortion. I don't know how you cannot find information explaining why higher order distortion is more audible. This is a readily known thing. Higher order harmonics will not be masked by the primary tone. That is for tones. They will be masked in music. For pure tones, Fletcher-Munson comes in again, because at low frequencies, the higher order harmonics will be areas of higher sensitivity. But SS amps typically don't have much distortion at those frequencies. Keep in mind with pure tones, the masked harmonics will themselves mask the higher orders for typical distortion profiles (to a point). That coupled with music again limits the practical audibility of higher order harmonics of real equipment. Philelore.