Best set-up under $20K

By the way - I have the Hegel H590 integated amp.  I got it to drive my Harbeth 40.2’s because Harbeth uses the Hegel amps to demo their speakers at shows.  It does a great job at controlling the Harbeths, which many amps struggle with - it adds clarity and resolution.  
 

You can bypass the internal DAC to use an external DAC.  I use the Schitt Yggdasil , which is superb.  I assume you can do the same with the H360.  Which is why I suggested to stay with it for now.  You can upgrade later if you need to.

Keep the Hegel and get a pair Harbeth SHL5 XD, or 40.2’s, or 40.3 XD at a discount.  Get a good player - such as the Bryston BDP-3 and with a Schitt Yggdrasil DAC or any number of others that will cost more). 

Or… keep the Hegel and get the Legacy Audio Signature XD, or Focus XD with a good player and DAC (suggested above).

Or… keep the Hegel and get the Klipsch Cornwall IV, or Forte IV speakers with a good player and DAC (suggested above).

Any of these will sound superb.  The Harbeths will have a warm rich sound a lot like the Quad ESL 57’s (about the best there is with proper set up and room), which is why I suggest them.

The Legacy’s a bit more neutral sound, with superb soundstage and bass as well as mids and highs.  Very dynamic with great detail resolution, which is natural (not hyped like the B&W’s).

The Klipsch also has great soundstage, mids, bass and highs with a live sound that will fill the room.  But, are pretty sensitive to placement.  They are very efficient, and can be driven with tube amps, if you want to consider some of those - probably best with tube amps.

Those would prolly be my top 3 in that budget range - some quite a bit less.