Also my amp has a very light buzz from time to time on my left channel.
Likely a tube.
I also have the BHSE, but I haven't compared it to other electrostatic amps. I recently swapped in a new set of tubes after feeling the sound was getting a bit soft. I'd been on these tubes (NOS Siemens) for two years of heavy daily listening. The new tubes (a set of Sofia Electric EL34-ST tubes) gave the amp a nice sonic refresh.