I live in Milwaukee and work right by ohare and I do the round trip almost every day in my P85.
It is doable but with the vampire load you're right that's cutting it a bit close.
Try some of the remote parking / rent-a-car places. There are a few that have 110v available. Try Thrifty, hertz, avis, etc. Otherwise a bunch of Kohl's and Walgreens stores have J1172, you only need enough to get home.
Generally the drive back up to Milwaukee is slightly more costly in WH/mi than the drive down. I get 280-290wh/mi down, and about 300 - 310 on the way north depending on traffic.
Worst case, the Villa Park service center isn't far away from ohare. They have HPWC that run at 80a. 53mi of range per hour of charge. You shouldn't need to stay long if you can get there. My drive is 88.7 miles each way, I'd go for it with 100 miles of range and just keep the speed to 65-68mph.