Interesting Jarek. I know the BHSE well, I ordered it twice, but cancelled and got a nice DIY KGSShv Carbon instead. The BHSE does have EL34s on the final stage (of it's 4 stages). The problem with electrostatic amplifiers is the voltage, you need to swing 1,600 volts. It is very difficult to design an all tube electrostatic amplifier without the complexity and lots of heat (many tubes).
Kevin Gilmour has the Circlotron, and also a Megatron, which I believe is an all tube gain stage amplifier, but runs very hot, a space heater (as does the T2) , and in a complex circuit. Frank's low run DIY amplifier (owned by Jude at head-fi) runs rare tubes that are radioactive apparently, but safe. I think that is why Frank used those big tubes, to get the voltage swing. Interestingly, the Sennheiser HE-1 also has a final Fet stage in the headset. The Hi-Fi Man Shangri-La looks to be all tube using 4 300Bs, but it sounds poor IMO.
I haven't heard the T2 (Kevin version). Is is supposed to be top notch, and uses currently available parts unlike the original Stax T2, many of it's parts are now obsolete. The original T2 was a bad design, it got way too hot and proved unreliable. It also nearly bankrupt Stax. That is probably why there current amplifiers are so weak, playing it safe with small tubes inside the case. The current top Stax amp is the T-8000 but it is very poor sounding. It is based on an old design, so Stax seem not wanting to go forward on their amplifiers. Woo Audio WES is not great either, though I haven't heard the MK2. Oddly, the over complex Mal-Valve electrostatic and dynamic amplifier I heard at Munich 2018 sounded really good, but with 14 tubes was way too complex and got very hot. It also cost 15K euros which I though was crazy, the Genus is miles better for that price and is a full blown SET speaker amplifier.
If you run planers you open up things a lot. I had a top 009 system as you know, and went over to planers. For me, they give me a more accurate sound, real bass and super smooth treble details. Less 'in your face' treble than the 009 off the BHSE or Carbon amplifiers.
I would try the LCD4s out of the Genus, or the Viva Egoista. And the Abyss or Susvara are in the same league. To my ears, these 3 planers beat the Stax. It is a different presentation, but if you are used to hearing high end speakers, I bet you will agree with my choice.
I am curious what you decide to build. Some say you only need 3 Watts max for planers so could use the 2A3 tubes. But having heard more powerful amplifiers on the LCD4 I think 8 Watts is better. And bear in mind, the Abyss is about 50% less efficient than the LCD4, and the Susvara 50% less than the Abyss at least.
Keep in touch!