I finally had the chance to get to the library last night, hoping to find the box scores for the games described on the poster that's been discussed here. I targeted 1934, as that seemed to be the year in which our discussion had been going.
In the Saturday Sept 22, 1934 edition of the Pittsburgh Courier, I found the box score below, and it's definitely not the same game as described on the poster (the article states that the game was Saturday afternoon). The Crawfords were in Pittsburgh that day, losing badly to the Homestead Grays 11-2.
I am going to look at 1945 next, in the hope that I can find something to support the idea that the poster is authentic.