Southwest's website doesn't work well (if at all) with overnight stays en-route. But sometimes you have to do it the old fashioned way: Do it yourself.
Book DSM-STL on Flight 546, Depart DSM 4:30PM, arrive STL 5:10PM. Sleep in the terminal or at nearby hotel.
Next day, on a separate reservation, fly STL-BZE on flight 4783, changing to 629 at FLL. Depart STL 5:10AM, arrive BZE 12:25PM.
This is based on a few random dates I picked in February.
When you have only a VERY few flights a day out of DSM, you are limited by whatever connections are still available at those few airports you can fly to.
Have you considered flying American?