Wow, $4332 for a month. That sounds pretty expensive.
Interestingly, there are a lot of things out there that don't seem negotiable at first, but you would be surprised how open a lot of people and businesses are to the idea. You just have to try.
It's not just about the money though. There are disadvantages in signing up a "guest" for a month. What if they are really obnoxious? Three or four days you can wait them out, but a month?
I would guess that people who stay for long stretches like that tend to look for full apartment listing, since the host might also be obnoxious, and it might get old to stay with someone for a month even if they're just neutral.