The last name on this list is another Yankees, Clarke Schmidt. In 22 games this season (21 of them starts), he has posted a 4.39 ERA with 99 SO in 104.2 innings of work. Over his last 15 games though, he has a 3.82 ERA and has credited a change in his repertoire usage for better results.
Why would Schmidt be a fit for St. Louis? Well again, he's a cost-controlled arm and has the ceiling to slot in as a very good number three starter or perhaps a number two at some point. For now, he would be a really nice number three or four starter for St. Louis
Some deal involving Dylan Carlson is where this could get done for St. Louis, but a combination of Carlson and/or some of their impending free agents could fetch St. Louis Schmidt along with some of the other arms mentioned before.