The worst crossover distortion I have had is with the first class B amplifier with its unbiased output stage in a high feedback opamp circuit. This distortion is audible as a separate not very music related, high frequency squelchy noise, which was only really noticeable on simple music, or with ones ear held next to the tweeter.

I belive that cross over distortion on its own is not that bad. A class B output stage is after all typically, two benign emitter followers which don't really have much of a sound. And after all, it doesn't necessarily happen that often. As music is made of various frequencies the more dominant lower frequencies will dominate the zero crossing point where the "glitch" occurs, leaving the "glitch" if there is one as a vaguely musically related noise. I don't think that this is the main source of the "transistor amp sound".

Low order distortions add a hardening to the sound.

Even order distortions do not sound nice.

Even order distortions are not responsible for the "single ended" sound.

For that you have to look else where.