My response:
Yes. Call any lawfirm in Illinois to ask for the name and phone number of their "Attorney Service" (those are the people that take pleadings to court for filing) and call that Service. Give them all the information about the judgment that you have, and have them go to the court to get you a copy of the judgment. It's far cheaper to do it that way, than to fly to Illinois, wouldn't you agree ?
IAAL