Soft, smooth organic SS integrated amps?

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.