I appreciate the math in the OP, but I really suck at math, failed algebra, and have a system that works for me. I set the volume at a comfortable level, with the tone controls flat, and then I add tone, usually quite a bit, because I like strong, authoritative bass and the clear quality of the bright part of the signal in the treble range as well. Then I ease up the volume to distortion (This is if I'm doing more than casual listening, which is rarely; I like low-level seshes.) and then back off the amount it takes to eliminate the distortion, which occurs on the impact of the bass, bass guitar, or bass drum. This seems to work for me. I'm an EQ guy, I like loudness and usually extreme EQ because of my usually low volume settings. I find a lot of vintage products can be light in this regard. My speakers also can't handle mass doses of EQ, so it only works well at low levels. I never go over 10 or 11 o'clock on the volume knob, regardless of the receiver or preamp. Power amps usually get turned up to at least 7. When I use outboard gear in a pro audio rig I try to achieve unity gain (7 out of 10, no higher) across the effects and the trim (gain) on the mixing board, set the channels no higher than 7 as a reference point, then control the system volume from the masters, and never go above 7 there... That's how I do it, and nothing gets blown up, especially not my eardums.