I wouldn't even start with this psychiatrist. If this is what you are seeing now, this is what you will see later. Given that medications are involved there is a safety factor.
Would your pediatrician be able to work together with the Chicago psychiatrist--as in treat together using consultation/conference calls? I usually wouldn't recommend this arrangement but your geographic area does limit you more than most families and a concientious pediatrician who would work in close consult with a psychiatrist would be preferable to a psychiatrist who can't be bothered to pick up the phone.