Take that puppy for a nice ride. Get the rear end hot and then dump the oil. You want as much suspended contaminants out of the rear end as possible. It might be too late. The damage may have been done already.
Drive Noise is most evident during constant acceleration throughout the speed range. Coast Noise is when the car is allowed to coast through the speed range with the throttle closed but with the car in gear. Float Noise is evident while just bearely holding the car speed constant on a level road at any given speed.
Differential Side and Pinion Gear Noise cause noise during straight ahead driving and will be most pronounced on turns. Pinion Bearing Noise is a continuous low pitched whirring noise starting at a relatively low speed.
It will be hard to clean the rear end, short of (ideally) pouring in half kerosine/half oil, warm up the rear end again, and then dump it all out.
It would be wise to fill the oil back up, (without the additive) drive another heat cycle, and drain that oil again to check for more partical debris. Then fill the proper amount of oil with the additive, and test ride again. If the noise is still there, you can either turn up the radio loud enough to override the noise, or monitor it until it's so loud, you have to go for a rebuild.
And yes, if you read a factory manual, they do have an audio value that if you CANNOT hear the rear end noise using the radio at a reasonable volume, it is normal noise.