I was reading some more about possible problems, and I came across the possibility that it is a spun bearing. After watching some videos of people who have this problem and reading descriptions, I starting to think that's what it is.
So, all of you Grand Prix experts, does this sound like it could be a spun bearing? Pontiac Grand Prix Noise - YouTube
If it is, I'm leaning towards driving the car gently until it dies. Any input on whether or not that's a good decision?
Blairj