without the correct backlash it will destroy itself, not just make noise.

I have been told that the pinion gear and the ring gear are made together as a set, and must stay together... so you can't just swap one ( gear ). Gotta keep them together as a set.

Also, if you want limited slip, then you have to find a limited slip and swap out the parts. There are different types of limited slip.. clutch packs, cone clutches, lockers... so decide what you want then track it down.