Which DACs are known to be sweet/rich/relaxed?

I would suggest those incisive speakers and amp will negate DAC change. It is always happening that pursuit for clarity where suddenly the musicality seems to have gone and you spend listening time finding the faults rather than enjoying the music. I'm at a place now whwith tannoys and luxman that I like. There is clearer there is more transparent but I find myself lost in music more now compared to when it was all pres and monoblocks and a spaghetti junction. 

If I started over probably a 6w valve amp feeding klipschorn

@parker65310 When playing loud, cymbals become harsh and bright for this recording of Californication by Red Hot Chili Pepper: 

Robert congratulations on one hell of a system.

That said, I would look to your own words for guidance.

"Nothing wrong with wishing to mellow things out a bit if you’re in a large untreated room."

Transparent system, beryllium tweeters, rock music, loud.

I would spend my money on room treatments first so that you actually know what the system sounds like. Not the room.

My 2 cents

+2 on optimizing the room first. So much time and $$$ on a fantastic system and so little effort with the most important component. The room. Happy listening 

Ron 

+3 on adding room treatments.