Without responding to individual posts, here's the update:
Today, using my clamp-on ammeter, I found two EGCs that equally shared the vacuum's current, both from circuits that share boxes with the offending circuit. One was the 2-g box coming into the kitchen from the garage, which has lighting on a separate circuit, and one from the disposer/dishwasher MWBC, where the disposer switch shares the 2-g bpx with the over-the-sink light switch.
I opened both boxes and separated every EGC in each box. That affected the vacuum, so I took it back out of the circuit and reconnected the problem circuit's black back to the breaker (as well as the neutral and EGC), which allowed the lighting to come on. Then, with my solenoid tester, found one hot EGC in each box (telling me the two were still connected in another box) against the neutral.
That pointed me to the rest of the switch boxes on the circuit, including another 2-g box with the kitchen light's other 3-way (the first at the garage door) as well as a dimmer controlling the dining-room light, which did not turn on. I found the right EGC to disconnect, which stopped the solenoid tester from indicating the hot EGC. Ready for this? The wire I disconnected was from the dimmer itself.
Apparently the triac was internally shorted to its normally-isolated mounting tab, which is riveted to the dimmer's metal front plate for heat-sinking. I confirmed by reconnecting all of the EGC's, and testing between the dimmer's green wire and the box's EGCs. The solenoid tester indicated a full 120 volts. Replaced with a switch, everything was back to normal and the customers were happy.