Never had a limited slip additive make any difference in gear whine or not.
The type of diff you're running shouldn't have any bearing on gear whine unless it has more run out than allowed. Do you know what brand of gears you have in it....and how loud is the whine on a scale of 1-10? Gear noise on accel usually points to the pinion being too shallow. If you pull it out and clean the oil off the gears, paint it with the yellow or white marker grease then rotate it through. I like to paint the pinion gear only and then rotate it. The pinion will leave a nice footprint on the ring gear. If the pattern says the pinion is shallow, you can ad .005 and see how it looks. The easy way to do this would be to add the shim under the bearing race in the case instead of under the pinion. Unless they honed the pinion bearing to make it go on of off easier, you will probably ruin it trying to get it off. I use 'dummy' bearings that have been honed for an easy slip fit then when I get my settings, I install the permanent bearings.
