The hum is coming from the transmission cooler lines. I noticed the transmission fluid level was high, and corrected that by delicately draining a small stream from the main pan (it turned out to be high by 18 ounces - a bit more than 1/2 quart - checked hot per the operators manual). The hum is now almost constant when in park - when I touch the lines I can feel the high-frequency vibration. So, definitely something to do with the cooling lines, perhaps they are clogged, inhibiting the free flow of fluid and causing the hum. Maybe the radiator needs cleaned.

I wonder if the transmission senses the heat of the fluid and activates a valve to send the fluid to the radiator, or if it is sent there all of the time. The car shifts well and I haven't noticed any transmission problems while driving. I will continue my research...

(PS I drilled a hole (5/64") in my thermostat - that had no impact on the radiator hum.)