The pipe from the glove box to the air conditioner is a feature Audi lacks (for no reason), but every other VAG brand has. I did this mod right before the summer vacation, it is very easy and takes less than an hour.
5G1 816 311 A — pipe, $10
5E0 816 355 9B9 — valve, $6
I used this manual. The only difference is a slight shift of the valve, because of the passenger side airbag lock – I had to move it inward by ~3cm. The pipe goes in the only available position behind the box, nothing is squeezed.
The width of the walls is thicker than the clips on the valve – I had to cut out ~2mm, take a look at the photo below. The Dremel tool is a perfect match for this mod.