"Limited skip" does not lock up the second wheel in all cases. Pulling a TT it may not lock but slip and help out. They are usually a type on diff oil that is used that when a friction is create "sticks" probably and better word somewhere. The pucks with springs is called a positraction and acts like a ratchet and does lockup. These are not usually installed as OEM you want to you tube limited slip verses positraction.
Your case you may want to verify the diff has the correct oil in it and maybe change that out, the limited slip can be adjusted to be a little tighter not sure about your model.
Don't expect that a rebuild would change it much sence you say this has been since new.
