I just don't get what your test shows. Was the audio signal clipped?
I ask because my understanding of under powering causing speaker harm occurs when one trys to use too small an amplifier and driving it into clipping to get the volume up to desired levels. Clipping changes the duty cycle of the speaker from that of a sine wave to something approaching a square wave (or from say 70% to near 100%). The damage caused is from overheating due to clipping, not absolute power levels.