I think what I'd like to do, to make it fair to everyone, is have a limit on claiming right away -- like, let people claim 15 when the claims first open, and then let them come back in a few days or so to pick up more. That way people who can't be at the computer right when claims open will still have a shot at picking up some of the ones they wanted, and people who like to pick up huge numbers of prompts will still be able to do so.
Does that work for you? I know last time you were frustrated by the presence of a limit.