You likely bent some of the valves, which means the heads need to come off and at least rebuilt, or possibly replaced. Until the engine is removed and disassembled, and all other needed parts and repairs are calculated will an accurate estimate be given, ans this will vary from shop to shop.
The engine needs to be removed to remove the cylinder heads and this alone runs over 15 hours, then all the other labor time to deal with the bent valves, timing belt and other issues that likely will arise, plus parts you're looking at a minimum of $4000-$5000.
In the labor guide I checked it said that the labor time includes removal of the engine, so I made the assumption that the engine needs to be removed to do this job. It doesn't surprise me, Audi really crams those engines in there pretty tight.