I think Feldman straddles that boundary with remarkable balance. I haven't listened to his second quartet, but I've listened with intensity to his first (only an 1/½ hour work), and it's effective on both levels. It is non-traditional in its organization and its sonorities, but it has a straightforward structure that is simple enough for a lay listener to at least partly grasp in a single hearing, allowing them to appreciate it as an object of beauty. At the same time, its form and content are original enough to pique a more demanding student's interest. From the OP's description, it sounds like the second quartet is similar.
Feldman strikes me as a composer who has partly avoided and partly succumbed to the trap — all too common, as I see it — of deciding that the state of constant revolution that music has been in since about 1885 means that they can do anything they please and write music according to their own inscrutable (and often mechanical) system, shattering so many expectations so their music defies evaluation and nobody can tell them it isn't good. (The stories I could tell about some "composers" and their methods…) I blame the vast difference between the expectations of academia, which is the main supporter of contemporary composers, and those of the general audience.