You state that people can hear 0.3% distortion; that may be true for some, but the average listener won't hear 0.5%.
Who are you talking to now? I stated nothing of the sort. I simply made reference to a study that demonstrated an audibility threshold of 0.3% THD for crossover distortion in a solidstate amplifier with average test subjects - to counter your "factual" assertion that no one can hear even 0.5% THD.
In any case, speaker distortion is pretty much completely irrelevant when it comes to the potential audibility of distortion generated by amplifiers. Speaker non-linearity is typically benign, low-order and generaly completely negligible at low power levels (where they operate most of the time). Contrastingly a badly designed power amplifier can have the exact opposite characteristic - can generate high levels of high (harmonic) order crossover distortion at low signal levels.
In any event, any decent amplifier will produce far less distortion
Who said otherwise? What is your point?
Who said what is usually easy to determine from the embedded quotes; I was just having a discussion with someone who drank the audiophool kool aid; nothing more.
That said, I'd still recommend that the effort / cost involved in getting that last hundredth of a percent of distortion out would be much better spent on boosting the output power. To prove amp design excellence, build one that will survive running at full power into a dead short with no component failure - not even a blown fuse.
Low level distortion is almost always due to the output transistors not being biased properly. There's a natural variation in components that means that no amp will be biased correctly unless each one is adjusted manually or elaborate automatic biasing circuitry is included. Matched pairs on the output devices helps, but you'll still need to insure that the bias is correct and that the idling current through the outputs is sufficient to get them into the linear part of their curve. You've got to waste some power supply current here; that idling current is critical.
Low frequency distortion is almost always due to clipping - there's a lot of energy in those low bass notes and an underpowered amp will clip here first.
General "rules" for quality amps: a very low impedance, very well filtered power supply to start; the amp should be able to draw any "legal" amount of current at any time without the rails sagging. In my day, we did this with large power transformers, big rectifiers, and big filter capacitors. That might still be the optimum solution - improve on it if you can. Many references to amp design exist - all I'll add to what they may say is to insure that your amp has an odd number of stages in it. Why? Audio amps have large amounts of gain, and if there's any (even a tiny bit) of coupling from the loud end to the sensitive end, if it's out of phase (due to odd number of stages) it'll reduce the gain. If you have an even number of stages, it'll be in phase and you might just create a high powered oscillator.
And always remember that while the design and math is precise, the components you build with are not. Imagine a world where resistors are 10% and capacitors are 20% or worse. If your design can function properly with any combination of tolerances in the active and passive components, it'll be solid when you use the nicer components you can buy cheaply today. And never forget: simpler is better, the fewer things to go wrong, the fewer things that will go wrong.
PS: Regulation of the main power rails is not too important. What's important is that both rails track each other precisely. A transformer makes this easy; is your approach more cost effective while providing the same functionality?