Soft, smooth organic SS integrated amps?

I know you said solid state but you should give tubes a try. Quicksilver integrated. You’ll never look back. In you budget, hand built in the USA and amazing sound. Peace out. 

As a Sugden , Cary and Croft integrated owner, I would recommend the Croft Phono Integrated. It fits your sound and cost requirements, and with the sub of one  Mullard 12ax7 it is exceptional.  Since it is a hybrid  you will have to deal with one tube in the pre stage and 2 in the phono stage but no messy power tubes. 
The only down side is the lack of a remote.

modwright

Exposure 2010S, not 2010 or 2010S2. Ranges from $600-750 depending on options and condition. Read the Art Dudley Stereophile review. It's accurate to what I have found. It has sounded great with classic JBL L112 and also with Klipsch Heresy IV and Triangle speakers. It's very engaging while never being too brash. I've had many more expensive separates that didn't give me anywhere near this much musical satisfaction.

Good luck!

Another vote for Marantz++