Soft, smooth organic SS integrated amps?

Early Jeff Rowland Amps:
Model 1
Model 2

If you’re after a soft and smooth sound, just use stranded copper speaker cables. That will make any amp sound softer and smoother than it is.

All the best,
Nonoise

Try to find a used Plinius. New ones are pretty expensive. I was told to never get rid of my integrated 8200 MKII.

My Croft Phono Integrated certainly fits that description and is a steal at under 2k new. If you can do without a remote it is the definition of organic sounding but still with PRAT. 

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++