What you are describing is backlash. There has to be a little play between the ring and pinion so that the helicol gears dont constanly grind. I am not sure what the backlash is for your unit but I saw it in a recent thread. Its also possible that is is just worn and needs to be adjusted like you said with shims. It can be set easily but should probably be left to a shop that does it all the time. I get my new diff and CV axles tomorrow, did you get an LSD?