Where in the Chicagoland area will you be living?
Depending on the answer, you may find you don't need parking. Take the metra train to a spot you can get on the blue line CTA train which runs straight to ORD. Or you can take the orange line CTA to Midway. I'm an hour drive from the ORD employee parking lot (non-rush hour) and it used to take 10-15 minutes to get from there into the terminal. I can get to the terminal using the metra/blue line in exactly the same time frame minus the traffic headaches. Just something to consider if you can use the trains as an option.
If you want to get into employee parking here's the story:
Employee parking at ORD/MDW is controlled by the City of Chicago aviation dept. You have to go to their badging office in ORD with a completed form to get issued the badge. The city will only let employers with "property" on the airport badge their employees. A charter pilot that commutes out of ORD on commercial carriers can't get one because his employer has no gates or offices at ORD. Each airline/company that have employees using the employee lots, have a designated signatory. That person or persons are the ONLY ones who can sign/approve your application form in order to get the SIDA swipe card.
They will be the first person you will have to convince that a Sprirt pilot based in FL needs employee parking at ORD. If you can do that, you'll be wayyy closer to getting approved. I would check with the local gate agents you have at ORD. I would think they will be local employees who would definitely need access to ORD parking. Find out who issued them their application - you may have to deal with their supervisor, etc. With the reasonably small operation you have at ORD, it shouldn't be too hard to track down the signatory. That's the person you'll have to sweet talk into getting you a badge. If you can get it, the nice thing is the parking is totally free.
Here's a link with all the badging info and the form you'll need to get signed. Good luck.
http://www.ohare.com/badging/