Powr-Loks are noisier and crankier than Trac-Loks because they have more preload in the clutches, plus they have a ramping device that increases preload with torque applied... reverse torque as well. The viscosity of the oil has nothing to do with it. Bottom line, what you are experiencing may be perfectly normal. They are not seamless like the wimpy factory Traction-Loks. Even the almost seamless Truetrac will bark a tire or something now and again. But here are some checks:
Powr-Loks MAY need some LSD additive (which Friction Modifiers or FM that smith out the clutch "break-away" and make the clutches operate more smoothly). Sometimes just a synthetic oil is enough (they are naturally "friction modified"). Auto parts tires will generally have, or can get, the additive (ask for "limited slip additive"). They come in 4 oz bottles. The Ford, GM, Mopar and other brands are essentially all the same and do the same thing. If you can find the Motorcraft brand, it's a good one at a good price but don't be shocked if they offer you an AC Delco or Mopar-branded bottle. They come in 4-oz bottles and you don't want to add any more than you need because if you overdose, it can reduce the oxidation resistance of the oil (a shorter operating life) as well as reduce the effectiveness of the limited slip.
First, before you add anything, go out into an empty parking lot and do some tight figure-8s with light power applied and see if you consistently get some clicking, clanking, chattering or grinding noises. If you do, you should add some FM. One bottle. Go back out and do more figure-8s. That will mix the stuff up and get it between the clutch plates. Sometimes that takes a bit longer than a few figure-8s, so I suggest you drive it for a while even if you still get some chatter. If, after a week of driving, you still get chatter on the figure-8 or in regular driving, add another bottle. It really shouldn't take more than two to make it as good as it can be.
As I said, the Powr-Loks are a little more ill-mannered than the really wimpy factory LS, so you can occasionally get some chatter, tire barking, or other noises. You are hyper-sensitive to them now because you just had work done and you aren't accustomed to "normal" yet. There are always honeymoon periods for the more effective traction aids. You should drive something with a old generation Detroit Locker or Lock Right... you'd swear the rear end was grenaded every time you turned a corner.