This is a great post; it points out how America WAS different back in the late 1930’s, as evidenced by Major League Baseball. All Major League clubs traveled by train, and even though the use of sleeper cars enabled a team to travel overnight to make it from city to city, you could only get so far in a day by train. Therefore, there were no teams west of St. Louis. There were also no teams in the south. Of course, at that time the bulk of the American population was along the northern half of the east coast and in the midwest. In the south, while there were major cities, heat and disease were still factors, and the widespread use of air conditioning was still a generation away.
To accommodate the “long” trips from Boston to St. Louis, it was attempted to put in stops along the way, such as Cleveland (AL) or Pittsburgh (NL). However, back then, they “only” played 156 games instead of 162, which allowed for more travel days. In addition, the doubleheader was still in common use. So, if the Cards finished up a series with the Cubs in Sportsman’s Park, and then had a game in Philly or Boston, the league could schedule an extra travel day, and then play a doubleheader on Saturday or Sunday.
At this time the PCL (Pacific Coast League) was a semi-independent league on the west coast; I don’t think the teams had a formal affiliation with any major league clubs as a farm system. While some west coast fans considered the PCL a 3rd major league, it was the source of some fine AL and NL players. Joe DiMaggio comes to mind.
You are right about the doubleheaders. Browsing the standings I first thought there must have been an awful lot of rainouts in 1938. Then I realized they were scheduled that way. Most weekends most teams a doubleheader. Today the doubleheader has gone the way of the complete game pitched.