2005 Gt Rear Differential Whine

First--I would recommend not using the dealer for maintenance and repairs once the car is out of warranty. They typically charge quite a bit more than other shops, and you aren't necessarily getting any benefit for that, other than a blue oval on the invoice.

For your driveline work, I'd recommend checking with the local gearheads in your area to find a good driveline specialty shop.

I'm guessing they pulled the center section, but didn't pull the pinion gear (assuming they pulled center section because you said they replaced "bearings, shims, races". Most likely they tried to get rid of the gear noise by adjusting the backlash on the ring gear, but didn't try to adjust pinion depth, which is a bit of a pain in the butt. With 150k miles on them, it's possible that there is either sufficient wear on the gears themselves, or on your pinion bearing (which again, I'm guessing that they didn't replace).

I'm not sure you'll have any luck getting Ford to reimburse you; also doubt you'll get another dealership to support your argument that you should get reimbursed by the first dealer.

My advice: without hearing it to know how loud it is, I'd first suggest turning up the stereo a little. If it's too loud for that, I'd suggest finding a new shop that specializes in drivelines, and having them go in and set everything. I'd seriously consider a new gear set while you're in there. Gears are cheap; it's the labor that's expensive, and you're going to pay that labor anyway. May just be time to upgrade that ratio while you're in there.

FWIW: I'm getting gear whine on my 13. I put 3.73s in a little while ago; also swapped them into my 95. Great gear, but it seems to me that these 8.8s whine when you hammer on them, no matter how well you set up the gears.