Call some of the privately-owned remote lots. If you are forced into a situation where you have to pay, they might offer something better than the airport parking if you can't find anything else for free. I did that during my IOE since it was only for one week. At MEM, the SIDA badge gets you in and out of the lot, but mine was still being processed. After calling around, I found a crew rate at another lot that was much cheaper than the long term airport parking.