Output shaft/inner CV joint
 

I noticed, towards the end of a several hundred mile journey, a humming had started from the front of the car. It's independent of steering angle, engine speed or load and is directly proportional to road speed.
I lifted the front wheels off the ground, and with the wheels spinning it sounds like its from the diff area of the gearbox.
There had been some dampness around the output shaft seal area for a while, so I checked the fluid level, and there's still plenty in the box, and what flowed out of the level check plug was clear and red.
I noticed that there seems to be a lot of play in the inner CV cups - they'll move around 1/8" at the outside end in any radial direction. Are these just supported by the splines on the stub shafts?

I just had same issue, the inner CV joints were loose, not a bad job to replace the drive shafts. It solved the shake on the highway when I lifted off the throttle, my hubs are fairly new, it was suggested they could be suspect, I went ahead and change the shafts, no more noise or shake.
While your at it , change those output shaft seals

I would look at the flex pipe first.