That's a bit nuts that they aren't being accommodating considering people don't want to take Uber or Lyft as they did pre-pandemic. When I was SFO based WAY before the current phases of the airport, if you got to long term lot and it was full (the SFO airport operated long term lot), they circled you out the lot before the parking ticket entry gate and someone handed you an exit voucher for the standard lot. Long term rates in the daily lots for up to 14 days.

Another option I just did for another airport. Find a Hertz or other rental agency with good rates for AAA or any other affiliation and do a one way rental car from your home area to ORD and then do the same back. (you only need a family member or friend to pick/drop you from that location - some Hertz locations if you call will pick you up and drop you) - Generally it's $50-90 bucks each way, CHEAPER than ORD daily parking even on needing a car to get to the airport and on the return.