It shows up in every power measurement I perform. You can see the shape of the overload. Sine waves in time domain on scopes are not as revealing due to pixel limitations and lack of dynamic range.
No "shape" of the overload or recovery "shows up" in any of your reviews. Maybe there is a "scope plot" on the AP CEA burst test you could push into overload and show the recovery?
Seriously, how can I see the "shape of the overload" (?) from your power measurements?
Short answer: you can't.
Here is how it was done in the late 1970s by HiFi choice in the UK- for
every single amplifier they tested. Notice the "shape" of the overload? Overload recovery was tested at various spot frequencies (published 1KHz) with asymmetric (diode clipped) 20mS bursts every 100mS. Amplifier was driven to half rated power and each 10dB burst took it 7dB into overload.
Quad 405 power amplifier
Sansui AU-1100A integrated amplifier
Pioneer SA-9900 integrated amplifier
FA-600 integrated
Sony TA-3650 integrated amplifier
This was regarded as a typical overload situation and a very useful indicator of overall stability. Some amplifiers do very well, others do very poorly. Some recover instantly, others do not. I use somewhat similar approach, but use the EIA/IHF 1KHz toneburst with both symmetric and clipped with a 20dB range to take the amplifier 3dB into clipping, over and above rated power.
These signals are trivial to generate these days and are used with purely resistive loads of 4 and 8 ohms. They pose no risk of damage to amplifiers, regardless of their age or quality.