Thank you. I had backed up to 1.8.3 without success, but updating the Board Manager fixed it without resorting to the "old bootloader" option.
Doing a simple test, I notice that the LED on the Elegoo Mega does not behave like the LED on the Arduino Nano (UPDATE: I forgot that the Mega drives the LED with an external buffer). It's always on, though it seems to be very slightly less bright when set to either INPUT or INPUT_PULLUP. I thought that the 2560 had the same internal pullups as the 328. I'll have to look for their schematic.