I had an other look at the Aetherwellen page.
Although it is not clearly stated, it seems that the proposed modification for issues nr 9 and 14 could solve the non mute issue.
The curves show a minimum level around -87 dB.
Issue nr 9
In addition, it seems that the audio signal cannot be reduced accordingly when playing at very low volume; the cut off distance can not be adjusted properly.
...
Solution : Include volume-control improvements as already advised in the EW modification documentation according to the original designs of Leon Theremin – all is now included at the CVC-Theremin VREB-10-2021] (Volume Rockmorizer Extension-Board)...
Issue nr 14 :
Volume control circuit of the CV-C Theremin is extremely sensitive to deviations of mechanical and electrical tolerances, inserting the proposed Wave Blocker is likely to change the cut-off position of the hand near the volume-antenna. It was noticed that complete cut-off did not occur and was not adjustable at the volume-oscillator tank or the volume control-voltage amplitude defining trimmer R57, located at the volume-oscillator board.
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To overcome all this, a dedicated piggy-back board (CV-C Theremin VREB-10-2021) was designed to minimize the additional stray capacitance, provide at least trimmers for cut-off (R59) and control-voltage amplitude (R57), hold the antenna extension-coil (L15) and the 320kHz blocking parallel-resonator (2x 470uH / 220pF).
...
The CV-C Theremin will now (probably for the first time) work correctly applying the Wave-Blocker, when volume-oscillator tank, volume control-voltage amplitude trimmer R57 and especially the cut-off trimmer R59, which has a big influence on the low-level volume response, are adjusted correctly.
I'm able to make and install this piggy back circuit but this will of course void Moog's warranty.
So It's a big and difficult decision to make !