Just to be clear, the phone is powering off by itself when on the charger after it reaches full charge. The fact that an alarm might be set is irrelevant - the phone shuts down completely. I have no task killers running, and I believe this behavior started after the OS update. It happens frequently, not just once or twice. Yesterday, it did it in the afternoon after maybe one hour of full charge - so apparently it doesn't require a whole night to act up.
I'm going to check how long I have to bring it in under warranty - I'm not in any hurry because it might get cured by another update. It was purchased new last month from Costco, on Verizon, and the paperwork is here somewhere . . .