I think it is highly likely we will have to play those final two games against the Tigers. If so, would they be in St. Louis or Detroit?
I agree. All we know for sure is that Detroit would be the home team.
My speculation: St. Louis ends the regular season at home while the Tigers end in KC. The most fortuitous answer would be for the Tigs to swing through St. Louis for the day on their way home and into the off-season.
Another factor is that the Cardinals will already be in their pre-playoff bubble, which would be complicated by a road trip to Detroit before they travel to Texas.