Ok, I'll answer my own question - I remembered I had an old TV card here somewhere, so I found it, plugged it in, installed tvtime and had a look. PCM Audio is working out of the box. ALSA mixer can control the TV card's input volume, but you can't control the ALSA mixer from tvtime (trying to change the volume has no effect), so that seems to be the issue.
Ok, I'll answer my own question - I remembered I had an old TV card here somewhere, so I found it, plugged it in, installed tvtime and had a look. PCM Audio is working out of the box. ALSA mixer can control the TV card's input volume, but you can't control the ALSA mixer from tvtime (trying to change the volume has no effect), so that seems to be the issue.
Is that your issue as well?