I've got the exact same issue with my 07. Extensive googling has indicated that the Draw-Tite 24770 (for '06+ GTIs) will work, although no details on what's required to install other than it takes '10 minutes'. Managed to locate a picture of it in action too:
I don't wanna go to the trouble of ordering it however, anyone else have any experience with this on an A3?
Dave