I fully agree and understand the privacy issues, not arguing this either at all.
If I understand the mechanism of theymos' give away system it is to un-link addresses from user accounts. This would function well if giving out 100 free stickers to 100 users. I would just get a random list of 100 addresses to send the stickers to and would not know which address was any particular user's. However with only one item shipping and only 1 winner, it would be painfully obvious who's address it was even if it was "unlinked" by theymos' redemption system. Furthermore, shipping a package (with some assumed value) requires certain information to send and receive in many countries. It would be very nice to maintain 100% anonymity, but when it comes down to it the package has to go somewhere to someone. Other solutions are 3rd party shipping receivers such as rental boxes, PO boxes, or figure out when your neighbor is out of town and give me their address instead then take it off their porch.
Mocacinno is already testing this system, with a list of a few participants:
https://bitcointalk.org/index.php?topic=5226618.
He explained there how
it works it
should work
I think it could be applied here also, but it's just a suggestion. Of course, you have the call on that. I just wanted to point how it is supposed to work.