Solid state amp that tube fan can be happy with?

Not likely. Man up and accept whatever is bothering you about tube amps.  I'd replace your EL34 amps with a nice DHT amp.  Aric, Apollo, Decware, etc.

The only SS amplifier that I would even consider is the FM Acoustic.  Nothing comes close.

 I don't own one, but I have read several reviews that imply the Modwright 150 has the warmth of tubes with the punch and control of SS.

There are a few Hybrid amps out there that have tube inputs and Mosfet outputs.  I have a pair of PS Audio BHK300’s that use 6922’s in the input section.  And there are a lot of 6922 and 7308 tube you can roll and get the sound you like.

All the best.

I agree with @atmasphere here. Get a nice pair of class D GANFET monoblocks like from orchard audio with your tube pre. It works great in my personal experience.