One of America's lesser brands was able to keep pace with Big Three automaker styling at the end of the 1930s. That company was Nash, at that time part of Nash-Kelvinator Corporation, an automobile / home appliance combine. A fairly detailed description of 1939-1940 Nash models can be linked here.
The first link, from Wikipedia, mentions that "George Walker and Associates and freelance body stylist Don Mortrude" were responsible for Nash styling at that time. Walker became Ford styling vice president in the 1950s.
Below are images I found on the Internet comparing Nash with some of its Big Three competition. Note the similarity of the general forms of the cars.
Both designs shown here are more advanced than those for 1939 model General Motors brands, despite GM in those days being considered the style leader in America. Moreover, they are better integrated than 1939 designs from Hudson, Studebaker and even the Chrysler Corporation's brand portfolio. The only retrograde styling feature on the Nash was the hinging of the rear door.
Two years later, GM was back to ruling the styling roost. Yet Nash was still able to keep up with the leader. Also note that the Ambassador's rear doors are now hinged on the center post.
More views of 1941 Nash models. The vertical 1939 grille theme has been replaced with a more horizontal layout, though the upper sections feature vertical bars. The four-door sedan in the lower picture has a rear-hinged door. It was shown open so as to reveal the folding seatback car-bed feature touted by Nash through the 1940s.