It's possible that nothing is actually being overloaded. The peak LEDs may be set to trigger at the point where the incoming signal reaches 2V RMS, but there may still be some headroom as a margin of error. The Beresford manual says "turn down the level of the signal coming into the CAPELLA inputs where that is practically possible if the Peak Detector LEDs are constantly ON".
"Constantly" suggests to me that there will be at least some headroom beyond the point at which the LEDs illuminate.