Research AC voltage to understand multi-phase (2,3,6) voltage

When increasing volume are you using a fixed tone or a varying tone? When you use a fixed tone the system (coil-motor-etc) operates at a steady state which is measured as "unchanged." If you measured from a full uncharged rest to full discharged stop you might see something different though. If you use changing tones (music), transients, and a few other items you will have a large change in the drivers performance. For example with music you could be producing a 60hz tone at one moment then 30hz at the next and could be at any step of power (speaking about subwoofers). This change could happen at any point in the travel of the coil so you may be sending full power to the driver at either an already full field (deep in the magnet) or at nearly when the coil is out of the gap.

When you think about it, its pure luck that speakers sound as good as they do

Yes, mostly just speaker technology, though there arent many amp companies pushing to change things. Class J amps are interesting, but technically it takes two of them to be sonically the same as a Class A or A/B amp.

Not an engineer, that I know of that is.

edit - Sorry if anything sounds a bit complicated in there, just woke up after over 100 hours work in the last 6 days..