Just throwing out ideas here...have you tried
http://portal.hud.gov/hudportal/HUD?src=/topics/homelessness ?
Humm, you can hang out in libraries and coffee shops during the day when you aren't working. And otherwise you will be working...
So basically, you just need a place to bunk for the night.
Maybe the idea of a storage shelter for your stuff is a good idea then? You only need to do it for about a week.
Or going to a camp site? Camping out for a week? They have restrooms and showers and things there... sucks sleeping outside, but you could manage it.
You just got to get to the 9th. And to do that you just need a place to sleep at night. Kind of like an adventure! It isn't for that long... and most your time you will be sitting around in shops or other places with AC anyway (with internet access!).
You can do it
One of my classmates last term was sleeping in his car at nights because he was so busy. He wasn't even homeless! He just needed to work and the labs closed at night...so he just did what he had to do to save the most time. You definitely can do it!
You definitely have options. They aren't the most fun (and you might feel like crap all week), but you will get through it and once you get your paycheck you will be over the hurdle and be ready to move into a new place (get that set up as soon as possible).
