Wow.... 66.6k close votes at SO, and despite my willingness I cannot assist in revising them. It certainly makes sense that only >3k users who can vote to close can also review these votes, but I assume there are many users in the range of something like 1k-3k who would like to help decreasing this number. So what about allowing 1k users to already review that queue, but requiring 4 votes by 1k users to replace one actual 3k user close vote? I think if in the extreme case 20 1k users agree a question should be closed, it is quite likely the 3k-ers would agree.
edit In order to make sure only those 1kers who actually want to help and not just get a shiny badge, disable the badge counter until they get to 3k.
edit2 Come on, do you really want this to reach 66.6k? Also, consider enabling this only for posts in the users' most active tags.