What new measurement can we develop to explain the difference in what we heard

[MasterApex]

Frequency and/or power response into an inductive load is probably the big difference here. Some amplifiers will have a more-than-negligible difference between an inductive and resistive load.
I would like to see a dummy load that simulates a 2-way ported speaker as part of testing.

This video mentioned variation in output impedance (segment 19:00) , power bandwidth (27min) and crest factor (50min) may be more useful that just THD once it is below 0.1%.

 

[Gorgonzola]

Speculating about the possibility that as of now non-measurable differences could potentially result in audible differences is not worth consideration until the existence of the audible difference has been rigorously demonstrated.

You'll understand that there is a cadre of sound difference deniers whose minds are quite made up. One fears that their investigation methods have been or might be tainted by their confirmation bias.

You'll also understand that they take considerable umbrage at may saying this.