Anytime you get to measuring power in big inductors there are lots of gotchas.
How about the definition of RMS itself?
A lot of test equipment assumes a sine wave and just applies square root of 2 to peak voltage. If the waveform is not a sine then the number is meaningless.
Since the load is varying the 8.3A shown by the DC power supply meter is some sort of average current. It can not represent a constant DC current.
I'm thinking a crude current foldover sum of the dual 8.3A DC input should get about 16.6A RMS on the amp output (RMS uses peak voltage not peak to peak).
The 23.4A rms isn't that far off from 16A.