Ah, sorry, perhaps I wasn't clear. When I said "I can use several different music players to play music remotely", I meant that I had in fact tried several, all with the same problem.
The problem even occurs if I use ALSA's own "aplay", like so:
$ amixer -c 1 sget IEC958
Simple mixer control 'IEC958',0
Capabilities: pswitch pswitch-joined
Playback channels: Mono
Mono: Playback [on]
$ aplay -D iec958:CARD=1 sample.wav
Playing WAVE 'sample.wav' : Signed 16 bit Little Endian, Rate 44100 Hz, Stereo
# Or aplay -D hw:CARD=PCH,DEV=1
$ amixer -c 1 sget IEC958
Simple mixer control 'IEC958',0
Capabilities: pswitch pswitch-joined
Playback channels: Mono
Mono: Playback [off]
Although hah, I just ran through that process again and the second time the On setting stuck.
Which I think I've seen happen before, but it always seems to go back to flipping off afterwards.