2. Theory #2 is the better because it accounts for the fact that it was
working pretty well: might the ALSA2Jack plugin have trouble handling
multiple streams at once? If so, is there a streams-mixing plugin I can use
before ALSA2Jack, to make this work better?
no, the only stream mixer in ALSA is dmix.
OK. Is 'dmix' already something which all ALSA streams go through? Or
is there a specific way to require it?
Ah, perhaps a clue:
This sound card is an ICE1724.