A feature to allow users to refresh the cache for just their flair. This is slightly more do-able
That would be quite useful, especially for the newly-initiated who move through the levels faster than established monks. Something like http://www.perlmonksflair.com/<username>.jpg?purge to force an update, perhaps?
You may want to keep an eye on how much that's used so that people don't put too much load on the server by constantly purging their badge, of course. Alternatively, you could do some sort of rate limiting for purging as well -- say, once per day, or (if you want to allow a little more flexibility) three times per day and seven times per week.
Thanks to both you and your friend for creating this, BTW!