The MOST LIKELY choice was to pass through Chicago and then take either a Union Pacific, a Santa Fe, or a Rock Island/Southern Pacific train.

About 1940 the most likely choices of these would be:

UP:
City of Los Angeles (streamliner, extra fare)
Los Angeles Limited

SF:
Super Chief
Chief
California Limited

SP/RI:
Golden State

There is a possibility he came through St Louis and Kansas City. I'm not an eastern roads kind of person, but at KC the choices are again UP, SP, and ATSF. The UP line, though, is different (until Cheyenne) than the Chicago-LA line.

For the deep south, SP is your primary choice out of New Orleans. Florida to New Orleans I again defer.

John