Here is some flight info if this is for your trip returning on Nov. 2nd.
It appears there is only one flight on AA leaving SXM a day and it is at 4:08pm arriving in MIA at 7:37pm, flight number AA2219.
Delta leaves earlier with a stop in SJU and there aren't direct flights to STL from there.
So you're going to have to overnight somewhere. Best to avoid a 3rd flight through CLT.
There are 2 flight options from MIA nonstop to STL on Nov. 3rd.
Flight #AA4408 departs 8:30am MIA to STL or
Flight #AA2226 departs 1:50pm MIA to STL
These flights are available on AA's website and there are a fair number of seats on all flights in 1st and coach.
If this ins't for your Nov. trip, never-mind. It was a good exercise for me.