With St. Louis playing three in Milwaukee, there is a civilized alternative to the tender mercies of the TSA or the joys of driving the Double Nickel and the Tri-State. The Lincoln Service offers convenient connections to the Hiawatha.
Northbound: 302 lv. St. Louis 6:35 ar. Chicago 12:15 transfer to 335 lv. Chicago 1:05 ar. Milwaukee 2:34.
A somewhat riskier connection for a night game: 22 (the Eagle from San Antonio, subject to Union Pacific's mercies) lv. St. Louis 8:30 ar. Chicago 2:14 transfer to 337 lv. Chicago 3:15 ar. Milwaukee 4:44.
If everything is running right, there is a connection for a day game, if you don't mind early starts: 300 lv. St. Louis 4:35 ar. Chicago 10:00 transfer to 333 lv. Chicago 10:20 ar. Milwaukee 11:49. There is strong coffee available on 300.
Southbound: 329 lv. Milwaukee 6:00 ar. Chicago 7:29 transfer to 303 lv. Chicago 9:25 ar. St. Louis 3:00. Time to walk to Lou Mitchell's on West Jackson for breakfast. Hiawatha 332 arrives Chicago four minutes after 303 leaves. Although I've bragged on those early arrivals, I don't recommend gambling on this. Amtrak, please note. The value of a hub and spoke corridor network is in the connectivity.
The next option is 334 lv. Milwaukee 10:50 ar. Chicago 12:19 transfer to 21 lv. Chicago 2:00 ar. St. Louis 7:36. There's a full diner on 21. Chicago readers: any suggestions for lunch near Union Station, should one want to go a cut above the food courts at Union or North Western? Greektown on Halsted is a possibility, but one really oughtn't rush Greek food.
Or have a leisurely lunch in Milwaukee, then use 338 lv. Milwaukee 3:00 ar. Chicago 4:29 transfer to 305 lv. Chicago 5:15 ar. St. Louis 10:45. Despite the suppertime departure time of 305, the train offers only a snack bar car. Buy a rib dinner at Robinson's in the food court and eat it on the train.