All the slack in a rear isn't necessarily backlash. Backlash is the amount of free play between the ring and pinion. Wear in the spider gears, carrier and stub shaft splines, and bearings contribute to the total slack. If it's just the backlash and all the other stuff is OK, the carrier can be shimmed over to correct the backlash, and it's not a huge job. SOMETIMES this causes a whine in the rearend no matter how well it's done. The gears are already worn and changing their contact areas make them noisy.
You can pull the rear and take off the back cover to inspect it. If nothing looks like it has much wear, it might be a good candidate to reshim, especially if it's a LSD or hard to find ratio. If it looks a little rough and it's a 3:54 open diff, I'd do like Denny says and find another, they are fairly plentiful.
John