Changed the transfer case fluid and the rear diff fluid. Both looked a little dirty, but OK. This had no effect on the noise. I guess the next step is to replace the transmission fluid as well. Still think the noise is coming from the center or rear of the car, but....
It sounds like a bearing noise, or possibly an hydraulic noise--a high pitched whine.
I saw an earlier post suggesting clogged transmission filters could also cause noise.
The car is definitely trying to tell me something, if I could only understand it!