More data: When the washer agitates, there is 119V AC across the motor connector terminals. As the washer continues to agitate, a rattling sound from the motor area gets louder and louder, and the voltage drops 118...117...116.... The washer agitates for approximately a minute, gradually getting lounder and with gradually dropping voltage, and then stops, sits there and makes a hum sound. The voltage at that point stays steady at 107V AC.
I have to turn it off, unplug, and let it sit there overnight before I am able to get it to agitate again.