I want to congratulate you for reading the Owner's Manual, which far too few people ever do. However, you have to go one step further, and read the other booklet that was provided, titled "Maintenance and Warranty" booklet--or something to that effect--for details on your Powertrain Warranty.
The Powertrain Warranty on my '02 Subaru was in effect for 5 years/60,000 miles, and it covered the differential(s), as well as all internal engine and transmission parts. I assume that your newer Subaru has coverage at least as good as what was provided in 2002, so you should be able to have this problem taken care of free-of-charge--as long as you have maintained the Tribeca according to the manufacturer's maintenance schedule.
So, rather than dicking around with it yourself, I suggest that you take it to the dealership for free repairs. Even if you are told that "no problem was found", having it documented on a repair invoice will give you coverage for differential failure even after the Powertrain Warranty has expired.
Don't even attempt to give the service department a diagnosis, because they are required to go through a standardized diagnostic protocol, and they will likely ignore a diagnosis that you provide. Just state the nature of the problem in full and let them do their thing.
Incidentally, you have additional warranties besides the Powertrain Warranty, and the now-expired Bumper-to-Bumper Warranty. While you are at it, read the details of your Emissions Warranty, your Rust Perforation Warranty, and your Seatbelt Warranty. You just might be able to save some money in the future on other systems, just as I saved you money today on your differential problem.