I have a pair of CLS speakers. I am a power cord believer for amplifiers. however, I haven't used heavy power cords on the electrostatic speaker.
The power supply to the electrostat puts....you guessed it...a static charge on the panel. It doesn't power the music so there is no need for short dosages of high current during dynamic sections. So my thought is that power cords are irrelevant and I've been using generic 14 awg cords.
Based on your post I will try better cords and see if I can hear any difference.
Jerry