My final attempt was to generate tons of periodic audio loops only a couple of ms long, and to play them back with looping turned on while altering each tag's volume in real time, hence doing a sort of additive wavetable synthesis. Unfortunately, looping is not a fully supported feature, and the only browser I found that does it (Safari) doesn't loop seamlessly at all.
All in all, my first brush with the <AUDIO> tag was a major disappointment. The <VIDEO> tag's high-level approach leads to similar limitations, but they are offset by the flexibility and power of the <CANVAS> tag. Unfortunately, there is no 'audio canvas' to solve similar problems with audio.