Did you spin the yoke by hand before you installed the rear end? If not try spinning it with your hand to see if it feels tightness or drag. My guess would be you have a worn out set of gears and there is no cure for the whinning if thats true. It could also be a bad pinion bearing. See if the pinion is loose when you spin it. It may have some in and out movement if the bearings are bad. If you where closer I would give you a hand.
When I had my 9 inch rebuilt I installed it and had the same problem. Returned it to my rebuilder - he installed a shim between the pinion gear and housing/ring gear and fixed the problem. Not a big deal, your just going to have to find a knowledgeable person in your area to repair. Good luck
Also sounds to me like the pinion bearing. Had one go out in a friends 8" (basically the same design, only smaller scale). We ended up just replacing the entire chunk, swapping with someone who knew how to rebuild it properly. Kind of like a core exchange I guess, but without having to pay someone for the install labor.
From what I've seen, it's not too complicated of an assembly, but you have to have the right tools to do everything perfectly. Good luck with whatever you decide.