Add headers to Output class cache files.

Headers are serialized and retained on cached files.

Original idea from #964, I translated it to include *all* headers instead of just the specified mime type. I don't know for sure how this will impact cached files; there may be different header conflicts when it comes to cache-control and whatnot. If there is any feedback that suggests this is a problem, we can easily revert it to only look for content / mime type.