Okay, I was a college student in Chicago starting in September 1971. When Amtrak closed the IC station, trains off the IC had to get to Union Station. Initially these included the City of New Orleans and the James Whitcomb Riley (now the Cardinal), which then ran via Kankakee and Lafayette on Penn Central.
Initially, the trains ran across the St. Charles Air Line and down onto the IC Iowa Line and went all the way to Bridgeport, where they reversed across to GM&O and backed through 21st Street into Union Station. Relatively quickly, they started running straight across the Air Line to Union Avenue Tower on the Burlington, which greatly shortened the backup move, but they did still have to back around the curve into CUS.
As far as I know, that's how the City and the trains to Carbondale are still doing it. If there was money available, the former connection between NYC and IC at Grand Crossing could be restored (it was used by NKP passenger trains to get to LaSalle St. Station). This has been proposed by the Midwest Regional Rail Initiative folks as part of their high-speed network. It might actually happen, though, because allegedly Mayor Daley is interested in seeing the SCAL abandoned so the area can be redeveloped.