Once the vehicle goes into drive/reverse, the engine switches mode - the ECU ups the ante with the turbo and adjusts the fuel flow to maintain RPM, since engaging gear would add some engine load (and even that is measurable, if you have an OBD adapter and an app like Torque). It's deliberate - to save the engine.
The difference between 'neutral' and 'park' is pretty much just the parking pawl - a pin that stops the output shaft from turning, but otherwise the gearbox is in neutral. As an aside, that's why (in an auto) you should always park the car, put it in neutral, apply the handbrake, let the car settle on the handbrake (take your foot off the brake) and THEN put the car into 'P'ark. Otherwise, there's constant pressure on the parking pawl and it can cause the end to burr - making it eventually quite difficult to get the car out of park.
So, the engine settles once the driveline is engaged. The inner portion of the torque converter would come to a stop as the clutches tighten in the gearbox (yes autos have clutches but not like a manual's clutch) and the outer portion would continue spinning with the engine.
I think that's where the problem will be. Either there's an imbalance in the TC that is quieted by engaging gear (indicating that the problem is most likely an imbalance in the inner part - or the output side - of the torque converter itself) or there's a problem with the motor.
I doubt it's the latter - if the car drives smoothly and has plenty of power without making a lot of noise then the engine is unlikely to be an issue.
Please let us know what Nissan say. They had a bit of a problem with older D40 torque converters engaging the TCC (which locked the driveline) - owners would experience a large vibration as the car passed the 80km/h mark and headed up through 95km/h but ONLY in drive with overdrive active. This was because in those cars (like mine), the TCC didn't engage until you exceed 75km/h, engine load is <50%, engine temp < 105C and > 60C, throttle < 50%. Meet those conditions and the TCC should engage, locking the driveline solid and thus saving fuel (no wasted RPM in the TC).