Bigamp, I think the magical sound comes from the very simple circuit topologies used in tube amps. If you look at a SS amp, there is gain stage after gain stage, lots of feedback loops, all because transistors are very non-linear and require a bit of correction to sound good. And as we know, less is more.
The characteristic tone of tube amps is more due to the quality of the output transformer than anything else. This is where the harmonics are generated and is the major source of coloration.
IOW, what I am saying is that with valve amps, the transparency comes from the simple circuits, and the lush tone comes from the output transformers. Remove the output transformer, and you get the transparency but with a more neutral solid-state character (like Atmasphere OTL's). The downside is that OTL's need a speaker with a forgiving impedance curve.
The negative feedback used in SS amps has the effect of removing low order harmonic distortion (2nd, 3rd, etc) but leaving high order harmonic distortion in place (7th, 8th, etc). Studies have shown that the high order harmonics are more objectionable than low order harmonics. Listening tests show that a surprising amount of 2nd order harmonic distortion is almost inaudible, for example!
In the end, the simplest amps sound the best, but place demands on speaker selection. The more complex amps are more forgiving of speaker selection, but do not sound as good. You can get complex amps to sound very good, but then you pay through your nose. Take your choice.