1) The UPS that was supplying the modem and router with juice died a horrible death. When I tried plugging it in anywhere else, the "building wiring fault" indicator came on with a continuous beep from the alarm on the thing.
2) The other UPS is now complaining exactly the same way it did last night, beeping four times every 30 seconds, indicating that it's running on battery power.
3) My UPS indicates that the voltage at the outlets is 137 volts.
4) My DMM says the same.
5) The manual for the modem UPS (which is an APC ES 550) says that it goes to battery power when the supply voltage falls below 89 volts or rises above about 139 volts. Two volts is not a big deal, but obviously the overvoltage is causing the UPS to freak out.
So I get to shut down the router and modem again. Isn't it wonderful?