Where is your doctoral program? Sounded earlier like maybe Alabama. You have until August so there is time.
Here is how I would accomplish it. Between now and June, don't make any more applications, get a PFD on the medical collection if possible and get your GF a secured card. In June sell everything you can in a garage sale. By everything, I mean everything, winter clothes everything. Put those proceeds on the secured card.
By then you might be able to use the shopping cart trick at Sportsman's Visa.
Buy a tent and camping gear. Less than $500. All of the colleges that I know of in Alabama with doctoral programs have national or state parks really close by. Hot showers, electrical hookups everything you need but air conditioning. Unless you're coming to Mobile, you will only suffer for about the first couple of months. As an example you can stay on the beach at Gulf Shores for $495/month all in. Just a small reservation deposit which you will charge to the Credit card.
So you can do the move for about $900 and live for 6 months at 1/3 of what the apartment would cost. By then your file will have aged and you should have no problems getting what you need. Also by then you might have figured out a way to pick up something other than minimum wage jobs. Temp jobs at the beach pay $20 an hour. Bartending gigs in B'ham pay $20 an hour.
