You asked me on MSN yesterday and I wasn't sure what the best idea was. I've though about it and here's what I'd do.
First install an invitation system. Rename the existing members group to Posters or Advanced Members or something similar and keep their permissions. All new members are put into a new group called Members or similar. The people in this group can only reply to topics, report threads, and create topics in the community areas, basically everything a Advanced Member can do except make a topic in the Downloads Area. To get into the Posters group and be allowed to create download topics they have to be invited by an existing poster.
Here's why I think this will work well. Registrations aren't closed and people can still reply to topics and participate in the community areas. No existing Poster will invite a Member to the Poster Group unless they can see they are active in the site replying to topics, engaging in conversations etc all stuff a bot can't do. This will really encourage Members to be active in the hope of finding someone among the posters to invite them. By Members being able to participate it's easy to get friendly with Posters too and get an invite as it can be hard to get an invite from a site that's closed like a private tracker. You can even run stuff like the Member who reports the most fake downloads or dead links each month get's promoted to Poster. Possibilities are endless. Great thing is your improving the quality of downloads by remove all the fakes and forcing people to be more active at the same time.