Audio amps really do not use anything like the nameplate power rating under all normal operating conditions, as mentioned above. If they did, and much of the power was converted into sound, you would be completely deaf and your Buttkicker would cause bits of your house to disintegrate. Thankfully the transducers are very inefficient, so most of the power is converted into heat. If your amps used nameplate consumption, the speaker cabinets would catch fire.
Typical audio program material is, as you are aware, very peaky, with significant consumption only going on for one or two percent of the time. You mention not being able to measure the instantaneous peak current with a clamp meter; if the peaks are too short to measure, they are too short to have any significant heating effect on the cables (or tripping effect on the MCB). With linear amplifiers the voltage drop incurred by the peak loading is important as it can cause the internal DC rails to sag, but with wide-range input Class-D (switched-mode) amps it is immaterial as they will work right down to 120V i.e. even 50% drop won't affect their operation. What matters to the cable and circuit rating is the average over the thermal time-constant of the OCPD and cable, and the figures can be surprisingly low.
Examples:
Quad 520 (normal linear HiFi amp) playing into KEF Concertos, excessive volume for normal listening at my workbench, audible from across the car park. Average consumption 0.3A. Yes, one third of an amp.
University rag week procession sound float. Basically a 40-foot artic with the combined mobile sound systems of three major universities' ents departments lined up along the side, probably 12 or more 18" subs. Attracted a police intervention within 5 minutes of being tested at 'low volume.' Amp racks included four Amcron Macro-Tech 2401s, probably six Yamaha 300+300W amps etc. Idling 12A, workable levels 18A, instantaneous peak about 30A (We reckoned to get away with a 2.5kW genny but the voltage regulation wasn't good enough because of the low power factor of an audio amp idling, I think we used a 5kW in the end)
These examples refer to linear amps. Class-D amps are significantly more efficient, and have higher power factor, so will use less current for a given SPL. I too will be interested to hear what kind of current you end up using...