Looking for recommendations for a 'warm' sounding DAC

Would anyone know of a warm sounding DAC, budget to £2500/$3000 new or used. My ears don’t like a crisp and clinical sound, I find that Chord/dcs/Topping sound painful if loud. I know many love those crisp leading edges that these deliver but that sound does not synergise with my amp/speakers nor my sensitive ears. I know the easiest way to achieve this would be to switch speakers to a mellow speaker but this option is not available.
Any suggestions would be welcome.
Agree 100% with Jackd. The Aqua La Voce S2 really warmed up my set-up (used it at the time with a Krell SA-400 Integrated into PMC Fact 12 speakers). Bought it used in the US (San Diego area dealer for about $2,700). It did wonders. Later sent it back to Italy through my dealer for a $1,000 upgrade to S3 (which sells for $5,000 last I checked). Since then, I was able to get my hands on a DarTZeel LHC integrated with built in DAC which bested the Aqua S3, but not by much.

Ayon Stealth or Stratos. Tube based out put stage. preowned cost is just above your budget. 
After a long declutter operation of ripping all my CDs and then recycling the jewel cases and putting the actual CDs into storage, I went further to detach a computer from the entire chain.  I relinquished myself and sanity to the streaming services and went though a year of hair pulling and natural age-related changes to hearing.  An innocent McIntosh MC5200 was jettisoned from my creative room in the process.  I even re-purchased some CDs that were packed away and lugged the Esoteric back from across the house to eliminate culprits.  In the end, ridding myself of the pre-diamond B&Ws restored my life.  There is watermarking and other issues with streaming and digital in general that seem to affect me more than others.  Later I found cycling through filter options on the various DACs I have attached to the current pre-amp / amp configuration offered additional relief for streaming.  The Esoteric reminded me I could probably do that with stand-alone DACs.  While I understand that in your situation the B&Ws are the immovable objects, instead of changing out your DACs, perhaps a vacuum tube amp might smooth out everything?  Nothing is more analog than a tube amp.  And they are also very social.  While my seemingly self-induced torture may seem nutty on its face, I play instruments 3-4 hours per day, for which I have zero ear fatigue but need hear to learn songs to do covers.
I came from similar sounding Dacs to yourBryston.  NAD M51, Moon 600 and a few others. That were all good. I was then introduced to the Audio Note 3.1. It was a game changer. So much more musical with no fatigue. Cymbals, piano, bells had a chime, ring that I had not heard before. A Miriad of speakers produced the same results. The difference was immediate. 


Thank you all very much for some excellent suggestions. I will be checking many of these out.