Arising, I too have an ESL system. I had Quad ESL57's, then ML, now modern Quads.
I have used tubes (good sound), and solid state (good sound). But here's the thing: ESL's tend to have circuits to protect them from high voltages caused by equipment failure (or owner failure, I suppose). They rob performance from your speakers. It would be great to remove them.
If you were to choose low power, high precision solid state amplifiers, it would be impossible to drive the speakers loud enough to engage the protection circuits. Therefore the protection circuits would be redundant, and so they could be removed. This I have done, running without protection circuits for nearly 10 years now. Practice is the same as theory - no problem. No problem whatsoever.
Caveat - my electronics are all ultra-stable full complementary push-pull home-brew, designed for low voltage and high precision. YMMD