Matt’s suggested approach works for this:
In your giveaway topic, link to a topic in a category that only logged in users may view, and explain next to the link users need to be logged in to view it.
I’ve used this very method to solicit feedback from neighborhood residences for city planning: we included polls for data collection, and linked to a topic with “prizes” (various links/coupons) provided by the city. We generated a decent pool of respondents that was easy to follow up with. 