Diff whine on my JK and I don't want to make it worse

My 2014 Wrangler JK has started making this low whining noise from the rear that gets louder when I lift off the throttle, and honestly it is stressing me out because I use it daily for work in Abu Dhabi and also take it out to the dunes most weekends. I changed the diff fluid last month hoping it was just old oil, but the sound is still there, maybe even a bit worse, so I am pretty sure something inside is worn. A guy at the tyre shop told me not to keep driving on it because it could chew up the gears and cost way more later, which makes sense but now I am stuck on where to go. I don't want to hand it to a random garage that will just guess, so I have been looking for an Expert differential repair shop that actually opens the diff, checks the bearings and backlash properly, and explains what failed instead of just replacing everything. If anyone has been through this with a JK or Grand Cherokee in the UAE, did you go independent or dealer, and how long did the repair take? I am hoping to sort it before the next desert trip.