Could you please enlighten us, not as to brands or products so much as to what traits those solid state amps have and what ICs/transistors they use? e.g., are there transistors that introduce the rich mellow sounds of even harmonics without other distortions? that provide the damping as to tubes? what other traits in the sound are you referring to? And what transistors/ICs are you referring to that must be at the heart of your systems? Any SS manufacturers that are generating a tubey sound must have at the core of their pre-amps and their power amps some unit that is identifiable across the board. Can you please help us with this?
I can, but you have to promise to follow along.
Here are the traits a solid state amp needs to have to sound nice and smooth like a tube amplifier:
1) it needs to have enough Gain Bandwidth Product to support the negative feedback the amp employs across the entire audio band. Depending on the gain the amp has, this value might be 10MHz to 20MHz.
In terms of what is measurable, this will result in distortion not rising with frequency, which is something at which most solid state amps fail.
2) the feedback must be applied in such a way that the feedback signal doesn’t get distorted before it can do its job. To this end, the base of a transistor or gate of a MOSFET isn’t a good place to apply feedback. For more on this see the writings of Norman Crowhurst. If the feedback is properly applied it won’t add higher ordered harmonics of its own, which is part of what makes solid state amps sound bright and harsh.
3) The non-linearities that cause distortion in the circuit should have either a quadratic or cubic nature, so distortion product tends to be lower orders.
This is obviously all engineering. Its doable. There are amps like this and unsurprisingly, sound a lot like a really good tube amp (actually a lot like real music). If you have any in-depth questions about the 3 topics I brought up, none of it is trivial and might require some study to sort out.