I don't think one should be able to request screenshots that are already claimed and submitted unless there's a serious issue with them (i.e., higher-quality print available).
If you request screenshots, you wouldn't be asking for a redo of sets that have already been submitted. Rather, you would let me know that you'd like to see that set sooner than later. And at this point I have sets that we may not get posted until next year! (Yes, I have that many backlogged.) The only thing I won't allow is requesting a set that you've submitted yourself as a way of getting yours up faster.
I have also set up a page where you can see what screenshots you've requested and their status. I usually only queue sets week, maybe two in advance, so if it's says that it's queued, then it won't be long before you can see them. Ideally I'd like to set it up so you would get an email notification once a set you've requested has been posted.
You'll find the link in the menu under "My IAD."