I have a 2003 350Z base 6MT with 50k miles. I recently had the 3rd gear assembly rebuilt under a third party warranty due to a failed synchronizer. Since the transmission was being rebuilt, an oem clutch and flywheel assembly was also installed. The car drives fine at local speeds; however on the highway in the ranges of 55-70 MPH a deep resonance frequency can be heard. While I have not pin pointed the sound, it seems to be emanating from the engine area. Any help would be greatly appreciated.
-The noise persists while the clutch is pushed in.
- Flywheel chatter is more evident even though it is an oem setup.

 

Might be your driveshaft binding. Mine did it quite a bit. Mine was more of a rumble that you could feel. Another option might be your throw-out bearing.

 

I had the exact issues ur describing but not on my Z, (on my truck). it ended up being my ujoints. i replaced them over a weekend, and eliminated the vibrating.

 

There isn't any noticeable vibration rather it is an audible low pitch frequency. The steering wheel and chassis have no noticeable vibrations.