These are awesome photos, and I have done a little work on the signs....

The Red Pegasus MobilOil sign suggests at earliest, 1930's, Happy Hollow Liquors & ButterNut Bread on right field fence suggest the repeal of Volstead Act, and acquisition by Interstate Bread Company (ButterNut/sign looks similar to Wonder). .

The most interesting is probably the Cook's Paint sign. Cook's Paint sponsored two AAU national championship basketball teams (1928-29), and owned a radio station in Kansas City (WHR?), 1930 - 50's.

The key, I feel, may be in the Frank L. Stephens Insurance sign. Though someone with access to a Kansas City Directory ca. 1930-40 for listings of Criterion Cleaners and Verdi Restaurant would probably be the most help. My guess is 1935-40.