Major cause of this is that the splines are/were not lubricated. Manual shows that the splines need to be greased when being fitted. Was there a rubber boot over the socket? If not, then that's why it got dry and thus wore. I just replaced the boot on mine as the old one was getting soft and cracked (135k). Take a look at this to see the arrangement:
http://nemiga.com/cat_spares/etka/audi/a4q/249u/260260/
The good news is that there are no broken shaft ends in there to have to pull out.
Before tearing into an engine removal, first thing I'd do is get the vacuum cleaner in the socket with a pick and clean up the splines and determine just how worn they are. "In theory", if the Audi designers used good design principles, the shaft should be a softer material than the socket and so should wear first. If so, the socket should not be "much" worn, and a new shaft will be sufficient. That said, how long did you run it with the spline slipping (that's what the zipper noise was) because under those conditions, the socket will wear some.
The only way to know though is to clean it up, measure the ID of the spline tips compared to the spline valleys in the socket to see how much "teeth" you have left on the socket. Compare that spline height to the spline height on the new shaft. If you have at least 50% engagement depth, then you can probably get away with not replacing the socket (engine removal) but instead swap out the shaft at say 30-50k miles as it wears.
You must grease the splines and fit a boot. The boot (079260753B) is secured with a 34.6mm Oetiker clamp (N10207701). You can close the clamp using a regular end snipping pliers such as you'd find at Home Depot and round off the sharp edges. I bought the $45 kit on ebay which includes all the sizes up to 24-ish and the pliers because I had other single ear clamps to fit. The shaft is 079260095D
(Note: after fitting the boot, you can still fit and remove the shaft - it just pushes through the boot. Regular grease is fine to use, or silicon grease or whatever you have laying around)
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