Aggrivated tinnitus from speakers?

Your speakers are bright. a pair of Harbeth die at 15k get them…

beside your speakers are not that good anyway, they won’t be missed

I’ll be blunt - WIIM is a POS and the McIntosh integrated DAC is as well (it’s harsh sounding). Add to this the KEFs and you’re drilling holes in your ear drums.
Since you will definitely benefit from a DAC upgrade, I’d start there. Try a warm sounding DAC. Go used. Denafrips, Lab12, even a Chord Qutest with the warm filter engaged will be more pleasant. Then upgrade your streamer. Get whatever room treatments you can deal with, especially for the first reflection points and tame the bouncing high frequencies. Play with speaker toe in as well - more direct toe in gives you sharper image but might reduce wall reflections especially at lower volumes and sound less irritating. You never know until you try. Good luck.

@OP 85dB is quite loud so listening at a lower volume level will help. However, improvements to room acoustics and probably a more refined speaker will too. However, I would still be careful with the volume levels. You may be tempted to play louder with a more refined speaker which, in the long term, is not good for your tinnitus.

I also have tinnitus, here's my path...I do listen to one or more of my systems most of my non at work life. First thing was adjusting my expectations regarding "perfection" and I recalibrated my Enjoyment Meter (too many of us think a thing is the end of the world, when it really is the beginning of a new era). I relocate and position my speakers in the main system more often than most folks, a pair of KRIX Euphonix (change seems to be a benefit in my case). I experiment with room treatment in my old house with very high ceilings, I use mostly tapestry and fabrics. I am using an SAE pre and equalizer system (not only because of tinnitus, but to compensate for years of ear abuse). I limit my high volume exposure (I never thought I'd say that out loud!!!). Hearing aids help with my tinnitus out in the world, but I seldom wear them while listening. I don't do much streaming, mostly as audition and background, (no television in my house) as I am a record/music collector first and an "audiophile" second. I watch my salt intake (something that I noticed for myself). When I do add to my systems I now tend to the British Sound, or more mids, and "softer".And finally, I enjoy the blessed days when the tinnitus recedes back into the background.

You have what they used to call a bright system.  Brightness is elevated  by hard walls.  Glass and brick. Some wire also leads to more high frequency  output. Interesting  you find the streaming worse than cd or lp. That tells you your streamer is bright. What do you have for a cd player? Turntable? Cartridge? Personally  I like walls treated with refraction  and only a wee bit of absorbsion. A thin curtain  a sheer on the wall behind the speakers  will help. Just for a try grab some bath towels and tape them on the walls at the first reflection  points. Find those with a mirror. Sit in you chair have someone  else hold a mirror along the wall and move back and forth  till you can see the center of the speaker. Hand the towel up at that point. The second  reflection  point is where you can see the opposite  side speaker hang another towel there. Listen  and see what you think. Then if you like that the quest becomes finding  the right material  that is even better and looks decent.  Before you spend anything  you cam try it  and see what you think. 

Regards.