Highway-speed hum in 2002 Golf TDI

I’ve got something that sounds a lot like wind noise at specific highway speeds, except that it isn’t. Starting at about 60 mph and ending about 70, there’s a hum/buzz that sounds a lot like blowing into a 2L bottle – about that pitch, and it gets louder/softer with speed, but doesn’t change pitch. But not wind noise, because if I put in the clutch, the noise vanishes. This may be psychological, but it seems to cause a bit of drag/friction – it seems to take more power to maintain speed in the humming-zone than on either side.

  • not wheel alignment or tire issues. Just got new tires, replaced a bunch of suspension bits (for unrelated reasons), good alignment. The noise didn’t change at all.
  • not wheel bearings; sound only when under power.

Something else in the drive train? Anything I can say to a mechanic to get them looking in the right direction?