Good freakin' luck!
I just went through the same thing, only all I wanted was a room for one night before I closed on my house. There was not a single motel/hotel that had a vacancy I could find (that I would want to stay in, anyway). I even had some gouge of a brand new Hampton Inn opening up by Unveristy Mall. The weren't taking reservations yet, so I knew I was good. I was calling about every 6-12 hours for two days. I called at 8am, no reservations...called at 3pm, they were completely booked. Grrr...
Basically the Navy lodge isn't taking anyone. You might be able to make a case for getting a room in the Q, since you're single and don't have anywhere else to go. Whatever you do, don't mention or even show your girlfriend to the front desk. Just have her wait in the car.
I was PCS'ing, so my orders might be a bit different than yours, but basically I ended up w/ a room at the NASWF Q in a back-up room with the understanding I wasn't staying long (one night). Apparently the studs get priority, second only to the Intl studs. Most of WF Q rooms are out of commision thanks to Dennis.
Good luck, and start calling early.
EDIT: Oh, if the P'cola Q gives you the business about not having any room for you, don't hesitate to escalate it and call up the Schools command duty officer (usually a stud waiting to start). There's no reason they should expect you to live in your car.