I ran a few tests today.

The wrist watch alarm is significantly louder when placed inside my cooking pot with the watch face down on the bottom of the pot and the wrist band fastened so it doesn't touch the bottom or sides of the pot. I was wearing a balaclava rolled up so there were several layers over my ears. Whether or not this idea will work when I'm inside my down sleeping bag, I don't know. I probably won't go out backpacking again until March, so it will be a while before I can let you know (I don't particularly want to sleep in a 20* sleeping bag indoors).