How flexible are they on that? Can you make it branded with some company that's sponsoring you for a period of time, or will that get treated the same as a block of regular ads?
Yes, I do tend to think that they would be tolerant of sponsorships, but I'm not sure I could find a sponsorship that would make up the difference.
You might be surprised - crunch the numbers to find out how many people are actually using it, then start emailing any relevant, big blogs, software products, services etc. If you've got enough traffic someone'll bite.