Grinding noise from transmission?

I have a 2007 Infiniti M35x AWD with 59000 miles on it. It’s a great car but for the last 5 months it makes a low-pitched grinding noise if I accelerate quickly from standing. The noise seems to be coming from under the car. It does not make a noise if I accelerate slowly or if I accelerate when in motion. I can feel the vibration in the floor of the car. Otherwise it behaves perfectly. The brake pads and rotors were replaced but the noise is unchanged. No warning lights come on, and the car handles otherwise perfectly. It happens on wet or dry pavement or in snow. I am certain it is not from the tires, although it seemed to be louder when the snow tires were on.

A mechanic at a trustworthy independent repair shop rode with me and thought that it sounded like the ABS engaging, but wasn’t sure. (He did not feel that the transmission fluid or differential fluid should be changed despite the recommendation by Infiniti to change it every 30,000 miles.) I took it to the dealership and they of course couldn’t hear it when they drove the car. (They did not think it was necessary to ride with me and probably think I’m crazy.) I can assure you that others have heard it when they ride with me. (I could still be crazy!) I decided to do some detective work and turned off various switches (Snow, VDC, etc.) and pulled some fuses. The only way to eliminate the noise was when the ETS (Electronic transmission synchronization) fuse was pulled. It seems to be coming from the transmission- perhaps the AWD is slipping?

So- what should I do, if anything about this? If there is something seriously wrong, I would like to get it sorted out. Any ideas? Thanks!