Ed, Midway is way out of my way unless I drive through the "Hood".
I would do that in my beater but not in a shiny object like the Lightning.
But....
If you want to make an adventure out of it and take two rapid transit trains we might be able to work that out.
The Orange Line train would take you from Midway to Downtown (Clark/Lake station) where you would transfer to the Blue Line train towards O'Hare airport. I'd pick you up at the Addison Street station, near where I live.
It would cost you less than $2, take just over an hour and is reasonably safe.
I'm planning on leaving around 12:30 on Thursday and going to the track first.
So if you get in around 11am, it could work very well.