I don't need, nor want, access to any data about unique readers/viewers. Is there a way of sanitizing the data? There is public data about pageviews so it seems to me that there should also be public data about media playback.

Alternatively, is there a way that I can file a request with someone who has the correct permissions to ask them to run the appropriate query?

The task Madhu pointed to is something we hope to get to soon, but we may find that we don't have enough hardware to host the extra data on the API.  Are the dumps a bad solution for this problem, though?  They're not too big in this case and not to hard to parse through for the small time period you're talking about.  The format is pretty simple too, I think you should be able to download and do everything you need with grep and awk.  Or python if that's easier.