It's an idea, but honestly I'm not sure there's a way to do what you guys want to do--make applications less of a hell for your team, and really no one can blame you for wanting to do that--while keeping the applications screened. Doing this will just add more work for you guys to do. I thought about suggesting this myself, but that's a lot of stuff to worry over and I eventually just went with the only idea I could think of that would add the least to your workload since commenting to the screened apps could also eliminate the need to keep a list of received applications (I mean unless people really want to see who all exactly is in waiting).

I really think that if you want to cap applications, you can't screen them. It is the simplest way to make the process transparent and completely eliminates the need for the list of received and processing applications, which is less work for you guys. Yes, there's a chance that people are going to throw a fit over X being considered and not them but there's that chance with any game that has an application cap. There's no way to avoid it, sad as is it.