So to offer a different perspective:
Firstly, not knowing your level of mechanical knowledge, here are some good reads ...
https://www.knowyourparts.com/technical-resources/drive-train/diagnosing-differential-noise/
https://fuelandfriction.com/weekend-warrior/understanding-rear-differential-noise/
https://itstillruns.com/causes-rear-end-whine-8454488.html
Diff whine comes in different varieties and depending on which type you have, you get clues as to what is causing it.
Diffs are not complicated but are precision devices in some respects.
In simple terms typical whines come from:
Lack of lubrication (have you changed / checked the lube?)
Worn bearings
Preload and / or backlash being out
Worn gears - although I would say this is generally unlikely with a stock engine (unless your car has done 300k miles and or been very abused). These diffs are pretty hardy. The spider gears in the R180 are the weak points but that shouldn’t introduce whine.
My advice is: having checked that there is enough lubricant in there, figure out in what conditions you are getting the whining.
Take the diff off if you are able to do it yourself and spend a little time on a work bench with some “engineering blue” and ascertain the wipe pattern. This will tell you a lot.
https://www.ebay.co.uk/itm/371441149605
This is a healthy diff that is currently on my car ...
Test the pinion pre-load. My old diff with probably 200k miles under its belt has 1-1.2kg of pre-load. New 3.9 diff with 100k had 3.2kgs and makes zero noise BTW!!!
Then if you are comfortable with using a DTI gauge, you can measure backlash.
So a good starting point is seeing how loose the diff is. Sometimes a preload adjustment will cure a lot of the whine.
Finally, the problem is, whatever unseen diff you buy is a roll of the dice. I can pretty much feel how healthy a diff is by hand - I have 3 in my garage.
If you need to buy bearings and seals, go to rockauto.com. Replace the seals if you have the diff out.
Removing the diff can be tricky but with some luggage straps and a normal jack mine went on and off easily ...
Other than that, as Jon says, the whine is something that takes me back to sitting in the back seat of my dad’s car in the 70s listening to the whine at motorway speeds. Something very retro about it!