Clearly the infinite switch (assembly behind the knob) had gone bad. Took 15 min to throw breaker, get tools out, take back off, pull part out far enough to see part number (leaving wire attached). Took 10 minutes to order new part on a Sunday night, it came on Wednesday, and I installed the new part pretty easily in 20 minutes or so. Would have been faster if I hadn't dropped a tiny screw.
Anyhow, the best news is that I fixed the thing for about $34, including shipping.