Google : Please let me run my filters on existing mail

My gmail inbox has admitingly gotten a bit out of hand.

I’ve got 1200+ (mostly) unfiltered messages sitting in my inbox.

I’d love to start filtering them, and in fact I have, but there doesn’t seem to be a mechanism in place to run a newly created filter over an existing mailbox.  At first I thought I must be missing something because it seems like a pretty standard thing to do so.  However, after finding this site, it seems I’m not the only one wanting this.

If someone has a solution, please point me in the right direction. Perhaps theres some API that I could access to programatically run a filter over the inbox?