The phrase "contemporary art music" has its own problems, of course. For example, it suggests that music from the rock and jazz worlds isn't "art" or "artistic music,"

I might be sympathetic to that objection except for the fact that it is virtually never raised against the term "art song" -- which is nothing but a special case of the same usage.

I've also heard the term "university music," since nearly all composers of the type you and I are discussing were trained in music at a university

The idea of "advanced music" (another candidate term, with its own problems) as mainly a university pursuit has historically been mostly an American phenomenon, but has started to spread elsewhere. In Europe the cultural milieu is different, so there hasn't been as much need for such music to "retreat" into academia (as it is sometimes pejoratively phrased). Of course, some composers (notably Babbitt) have explicitly embraced the university as an ideal setting for this sort of music, and don't mind terms like "academic" (considered derogatory by some).

On my university popular music course, we were told that the accepted term at that time (ten years ago) was "Western Art Music", but that that covered jazz as well. Possibly "orchestral" music? Although that would then cover stuff like film scores, or rock bands using a symphony orchestra as what amounts to a big guitar, and wouldn't cover solo piano works or someone like Varese...