It may sound silly, but what does the rear window look like? The rear window can slowly delaminate from the convertible top cloth, allowing moisture into the vehicle. Check that window/cloth connection thoroughly and let me know what you find. Thank you.
The rear of the TT is split into two compartments - one for the top, the other for the luggage compartment. The only thing that "separates" the two areas is a skinny piece of carpeted trim panel. Also, depending on where the boot and bootlid is damp, you can also check the following areas: trunk lid spoiler, if equipped, and under the carpet of the luggage compartment. The reason being that any moisture in the rear area of the car evaporates and makes things like the boot lid damp. Back to the spoiler, remove the bootlid trim panel and inspect the spoiler mountings. It is bolted to the lid. You may have a seal leaking water directly into the bootlid. I hope this helps. Definitely write back and let me know what you find. Thank you.