1) Feedback sucks. One thing that often makes tube amps sound better is greatly reduced or no negative feedback. All transistor amps need moderate to high levels of feedback. Transistors are inherently less linear amplifying devices and need artificial linearization to perform acceptably.
Let's think about this for a moment.
If you take a triode, and add a screen grid and a suppressor grid, you end up with a tube that has higher gain but is somewhat less linear.
If we work backwards from this, it would seem that a triode has some sort of internal feedback mechanism which linearizes the tube at the expense of reducing its gain.
Now, a transistor also generally has much more gain than a triode tube and is also generally less linear.
So what if we add a bit of emitter degeneration to the transistor, bringing its gain down closer to that of the triode which would also linearize the transistor?
What would the fundamental difference here be?
The difference, Steve, would be the loop length - if I take your word at its value and assume there *is* a feedback loop - I've definitely *not* heard things described like that before but allow that you may be right. I'm honestly not looking for a peeing contest; you may have something. But, the loop length is critical - as I'm sure you know - because a long loops means longer feedback times and the longer the feedback cycle time the more and *worse* distortion products created and the worse the sound.
One thing I do *not* understand completely is how or why tubes clip "differently" or "more gracefully" but this is *true* in the real world.
Care to show us? The Hamm paper seems to demonstrate in the real world that this is a myth.
I haven't read the paper yet but so far don't have too high a regard for it.
Tell me this: does the paper go into detail on the effect of FEEDBACK on distortion products?? It is, in fact, the high NFB in the typical SS amp that creates the higher-order, most objectionable, nasty-sounding distortion. And as was pointed out by Jon, in some ways at least this gets *worse* at lower signal levels due to crossover distortion which is a real recipe for disaster.
So, the very short answer to your question would be, and this is partly conjecture at this point, that the feedback-induced high-order products that SS amps produce when they clip is what causes this subject tube vs. sand "power" difference. Typical PP tube amps with low feedback (<= 10dB) don't have this problem.
I've also seen at least one paper demonstrating - with scope results - that vacuum tubes do have the ability to swing *much* larger voltages for very short intervals than transistors - this is a real, fundamental difference between them as output devices, and this would certainly explain a very real difference in "clipping" behavior.
So, I'll read the paper and it might have been smarter to do so before replying. But, if I were to read this morning a scientific paper in a peer-reviewed journal that explained to me in detailed, mathematical terms why the sky is red, I'd be inclined to keep believing it is blue.
4) Single-ended tube amps generally sound best of all because, in addition to running in class A (as do some PP amps as well) and having a natural distortion specra...
What exactly is a "natural" distortion spectra? Do you mean simply even-order dominant distortion? If so, what makes that somehow more "natural" than odd-order dominant distortion? Have you looked at the spectra of various acoustic instruments?
I will refer you to an excellent article by Nelson pass on this very subject. It amazes me that he does make PP amps at all anymore (market demands, I guess), as he so obviously prefers SE circuits for these reasons.
It's on the web - if you can't find it let me know. Think I have it saved somewhere.
...we are using very linear output devices that allow zero feedback and also great simplicity in the circuit.
Is there really zero feedback? Or is it really just an illusion because any internal feedback mechanism in the tube isn't drawn out in the schematics?
Much more the former than the latter.
I love to flip over my Fi 45 monos and look at the circuit - it's the input tube, output tube, and output tranny!
Have you seen Nelson Pass' Zen amp? Doesn't even have an input transistor. Just an output transistor. 
No voltage gain? Like the F4? Yeah, if you want a zero-gain amp you can make it even simpler.
I bet a zero-gain SET could be killer.