Solution A: Increase the number of admins, which will increase the number of deletions.
Solution B: Have a bot automatically delete files in certain categories that have been there since X days.
Solution C: I would expect that most problematic uploads come from new users. Disable the creation of new users (or their ability to upload) while the total backlog is >X files (no pun intended). Have a messaage displayed prominently to put social pressure on the admins ;-)
(disclaimer: I am not an admin on commons)
Magnus