Edited to add: For the next common "game" on this line "why dont you just walk past and card swipe exit" you will note the cameras positioned at the card terminals at all of these lots for this issue. Basically they will have a record of: your license plates for the entry/exists (the sipes and video systems have timecodes that can be matched) and of your person walking by on foot to trigger the exit state.
The cost of the zip car + the hassle of booking the zipcar, walking from to it to grab the card, driving your car out and finding parking, then walking back to the car.
I would emphasize that this method requires finding parking outside the parking garage. Around where I live, that could be a long walk back to the garage (and paying a meter...)
Drive your car in and take a ticket as normal. When it's time to leave, book a ZipCar for one hour. Grab its parking pass and use it to exit the garage with your car. Park on the street nearby, walk the pass back to the ZipCar.
Are there typically countermeasures in place for this? Match the pass to the license plate with ANPR? Don't allow an exit without a corresponding entrance? Sucks for the next person to use the ZipCar. But how will they know it was you? Are video archives good enough to find the plate associated with a particular card swipe without a ton of manual effort?
(Assume you're trying to store a car for a month or more. At a fairly normal Chicago visitor parking rate of $25 for 2 hours, that would cost $9,000.)