You might be thinking about a different truck. The sav bearings are equally sized on each side of the diff. I think you're probably right about it possibly being a bearing problem though. The bearing on the ring side HAS been giving people a bit of trouble lately, but a little shimming seems to help quite a bit. A friend of mine went through 3 ring side bearings in a week, till I finally convinced him to let me touch his truck long enough to shim the diff for him. I believe the excessive slop allows the shallowly beveled ring gear to exert enough lateral force on the bearing each time the throttle/brake is applied, that it eventually pounds the inner race right out of the assembly. You'll always have that lateral force due to the interaction between the ring and pinion's teeth, but minimizing the slop is like shortening a hammer's swing.

You might check your axle bearings as well. I've seen a few savages lately that have had rusty axle bearings right out of the box.

Here is HPIs .PDF on how to rebuild the Savage diffs. Kinda depends on what you're after, it's ok for general use. A couple of things I would add though are, grease the inside of the housing/gearbox to catch any foreign material that might make it's way in and seal the skidplate to the housing with RTV.

Click on this Google link and select the first result for a kinda generic how-to on diff shimming.

Good luck and have fun with it!