Dave, I like the idea of having a contest of some kind and think that would really make a sizable dent in the mountain of Unknowns. I don't think we want people to "adopt" them, though - that's what you do for a profile that you are going to work on. The Recycle Unknowns category are profiles that have been determined to be useless litter - they need to go away, not be adopted.
Another big problem area for the Unknowns project is all the profiles that have "Unknown" or some variant as the LNAB. Unfortunately, the bulk of these profiles are not available for adoption - they have managers already and, in many cases, are not open so nobody else can work on them. We're working on the ones that are open, trying to find names for them and we're also trying to get the managers to open the others so folks here can work on them. When we encounter an unresponsive manager, we're trying to get those profiles orphaned and opened, again to be able to work on them. If we get to a point that there are a lot of Unknowns that are open then a contest would be great for these.