LVB's Late Quartets -- I wouldn't mind the adagio from Op. 132 playing as I die peacefully in my bed... For a sharper take on LVB's late quartets generally check out the Orion Quartet (available on Tidal) -- they attack every single note -- very wiry and powerful . Kind of hard to listen to a "prettier" ensemble like the Tokyo String Quartet -- or, really, almost any other group -- after exposure to the Orion.
I second (third?) the referral for the Mandelring Quartet's traversal of DSCH's quartets (great in SACD). Generally speaking I love the way DSCH brings it all to a close in his last one, #15, which consists of six adagios. (I guess I like adagios.)
Speaking of finales, the 3rd movement of Britten's #2 is worth all 18 minutes just to hear them whack away furiously at the end. Bet DSCH wishes he had thought of that ...
In the category of Contemporary, Slow and Pensive, Vasks' quartets are worth exploring.
The Nightingale Quartet offers a well-recorded SACD series (also on Tidal) of Langgaard's output. Like his probably more well-known orchestral works, these are wide-ranging in style, from neo-classical to folk-inspired to modern.
I think everything I've mentioned here is on Tidal. One of the great benefits of Tidal for me has been the ability to explore beyond the usual canon. I've discovered a ton of northern European composers from the late 19th to mid-20th century who are every bit as listenable as their more famous contemporaries. A lot of it's late Romantic with some modern undertones. Wilhelm Stehhammar, Lars Erick Larsson, Joonas Kokkonen, Pohjola, Atterberg, Rangstrom, Halvorsen ... And while you've in Tidal you can find Andreae, Hindemith, Alwyn, Hetu, Godard and Gade -- also from the same periods and thematic range as those mentioned previously, also equally worth listening to as their more well-known/oft-recorded peers.
As for the warhorses, you sort of kill two birds with one stone by checking out the Guarneri Quartet's Red Seal recording of Mozart's Six Quartets Dedicated to Haydn, which includes K. 465 "Dissonent", the piece someone rec'd earlier. Swinging forward on the pendulum, DaCapo has an excellent multi-box series, Carl Nielsen Masterworks. The second box, devoted to chamber works, includes the two SACD's of the Danish String Quartet doing the four quartets. The rest of the (redbook) discs in the set are also well-worth a listen -- piano sonatas, some interesting wind chamber works, etc. For that matter, Dacapo's recent Nielsen symphony series with the NY Philharmonic is also first rate. Last I checked all this was on Tidal as well.
Parker