As someone who works a block from Chicago Union Station, regularly takes Amtrak, and also the blue line to ORD, I would agree with the previous advice and just self connect with WN. From Union Station to the blue line is a safe walk at pretty much any time of day (though I would recommend taking the slightly farther walk to the Jackson stop over the Clinton stop). Depending on time of day, an Uber to ORD is also only about $40-$45, so that's a good option. Problem is you would also need an Uber on the front end to get from STL to the train station. So now you are probably $30 (uber), $25 (Amtrak), $45 (Uber). So depending on how much you value your time, I'm sure there's a cheap enough stand along 1 way flight on a different carrier.