The charging/load-test indicated a few bad diodes in the bridge-rectifier.
I replaced the alternator and the whine is gone.
I doubt this remanufactured alternator will last 272K miles, but it has a lifetime warranty so it's all good.
Anyone getting ready to remove the alternator can save a little time by removing the radiator fan shroud and the radiator hose (after draining the radiator of course), since those need to be out of the way in order to get the alternator out of the engine bay.
Getting the battery out of the way makes things easier as well.
Thanks for your input StephenZ. Very much appreciated.
Mark