2 general suggestions to provide the lush, non "digital" sounding digital signal you want:
1 - Any resistor ladder (R2 R) DAC, as opposed to the more common delta-sigma design;
2 - And the ultimate R2 R variant: non-oversampling.
I own 1 of each, both DACs made by Audio GD, a Chinese manufacturer well respected & reviewed on Head-Fi.org in connection w/desktop audio. But I think these DACs are so good they would serve quite nicely in a big living room system.
My ultimate preference is the NOS 19, Audio GD's previous line of non-oversampling R2 R DACs. There are still a few left for purchase at Magna HiFi in the Netherlands (that's where I bought mine). This is my day-to-day DAC, and its sound is far and away the best I've ever heard from any digital device. I do a lot of listening through headphones, so I'm really hearing it all...yes, it's warm, lush, and dark. Also very musical, organic, relaxed. The bass is excellent, but it's not dry, as digital so often is. It sounds quite full and a bit "wet" (opposite of dry: rounded, slightly soft edges while at the same time dynamic & hard-hitting...a very pleasing sound IMO).
https://www.magnahifi.com/en/webshop/product/audio-gd-nos-19I was so impressed by the NOS 19 that I purchased the DAC 19, the non-oversampling variant of the same design (also from Magna HiFi).
New, shipped to the US, one of these units is ~$900. You can find used DAC 19's from 2015 onward (the latest software generation) for ~$600-$650.
BTW, either of these units can be configured with 2 X RCA output pairs--an extremely useful feature, at least in the desktop system, where I have one pair driving a headphone amp/preamp (to powered monitors + sub); and the other pair driving a 2nd headphone amp. After living with this convenience, I wouldn't want to do without it....