Has any experienced excess background noise if the dial goes past 12?

Yes, distortion stats take subjectivity out of the equation but do not indicate the final sound that will be produced with all components in use, being listened to with human ears... your ears. The THX amps you mentioned may have low measured distortion. But I remember that one reviewer noted that the 789's dynamic (peek amplitude) capabilities were inferior to his truly "first-rate" amplifiers. I'm all for being aware of a component's specifications. But I'll trust my own ears and "subjective" preferences over numbers... especially when using the multiple components that within a headphone system. The "wide range of unknown factors" become known if I hear them. Of course, "first-hand experience is incredibly helpful." Yes, a poor link in the chain degrades the whole. But I stand by my statement that one's headphones and amplifier are vastly more important than the system's DAC. (And it should go without saying that someone trying to attain hi-fi accuracy and/or pure musical enjoyment should not be listening to low-quality sources, such as low bit-rate files.) "Minimal distortion" is just one factor of many to consider when defining audio "accuracy". And always remember, human ears are not microphones or computers. We all hear a bit differently. "Clarity" and "warmth and thump" are at different ends of a distortion continuum. Incorrect. Clarity is simply a result of a component's ability to reproduce audio at a high resolution. Warmth and thump are characteristics of elevated lower frequencies and have nothing to do with "distortion". But I understand and agree that in order to achieve "accuracy in replicating the source", distortion should be minimized. Resolution and frequency response are not related, since a high-grade planar-magnetic (with superb resolution) can be tuned poorly (with inaccurate frequency response).

Re rating equipment: I rely on distortion stats. First-rate = minimal distortion. The equipment I've listed are excellent in minimizing distortion. Stats take subjectivity out of the equation. A statement of "first-hand experience is incredibly helpful" -- No. These are subjective and based on a wide range of unknown factors. All major components (source, DAC, amp, headphones) are critical. A poor link in this chain degrades the whole. IF one's goal is accuracy, then selection should be determined by minimal distortion. "Clarity" and "warmth and thump" are at different ends of a distortion continuum. The greater the latter, the higher the distortion. Many prefer distortion, usually at the higher and lower ends. That's fine. Others prefer accuracy in replicating the source. "Resolution is entirely independent of frequency response" -- No, these are related. Frequency response is a measure of a system's response to a source.