Yes. The farther the diaphragm moves, the higher the modulation distortion for a given SPL.
While this is correct, this has not much to do with efficiency. For a given SPL the same size diaphragm has to move the same excursion independent of efficiency. You cannot compare 4inch divers to 15inch or (bass) horn speakers and call this a difference in efficiency only.
2) How can you achieve higher sensitivity besides increasing the driver's physical diaphragm area...or the number of windings in its voice coil?
This is an interesting assumption and it shines some light on most of your statements/deductions.
Increasing the diaphragm dimensions will alter the speaker completely to the degree that a comparison becomes quite unreasonable, especially for woofers. You end up comparing 4inch drivers to 15 inch drivers. Apples and beers.
Instead one should compare like for like. So let's stick to direct radiating cone drivers of same size and impedance in a box.
If my algebra is correct this is the formula for (reference) efficiency.
Increasing the efficiency in this case will therefore be mainly an outcome of
- increasing the magnetic field (bigger magnet) [-> higher cost- > higher status -> probably the origin of the myth]
- decreasing the moving mass (lighter diaphragm or shorter voice coil winging)
The result will be a much different outcome regarding differences in distortion.
Using a bigger magnet is the most obvious way to increase efficiency without changing much else and that is exactly it. It will not change much in respect to SQ. But you have to adapt the design of course as Q will be different and that impacts low frequency response. There might be some effects from higher current (to compensate the weaker magnet) like hysteresis and flux modulation though. On the other side the bigger magnet is an obstacle to air flow and will create more reflections on the back,
A lighter diaphragm will have similar effects (more efficiency, lower Q) together with less bass form greater f_0 and maybe a different FR in midrange from a different breakup behaviour. Shorter voice coil winding will probably increase distortion.
So the answer of the OP is - as always - it depends.
As
@Mnyb mentioned, many compromises have to be made and that defines the result, not one number.
About thermal compression my opinion is that this is overrated. It is more of a slow effect, no kick drum beat will have less dynamic because the voice coil/magnet heats up during reproduction. Instead a woofer will get warm over time and thereby volume will be slightly reduced (from increase in R and decrease in B). For hi-fi systems with a sound pressure level that does not jeopardise my hearing, this is as good as negligible. (PA or deafening party with low DR music is different.)
And 80dB with 30Hz is NOT too low for a reasonable measurement. Excursion of that small woofer will be a bit over 3mm. If you want more SPL in sub bass you will have to use other drivers for sure.
100dBspl on the other side IS unreasonable as these volumes will put my hearing in danger if sustained for more than fractions of a second once in a while. Therefore it might be less challenging to measure IMD with high SPL, but it is in no way "more realistic". Certainly not for the Purifi driver that would be driven to (rather high) Xmax at 30Hz/90dB.