I also sent a query to the Circus Historical Society, and they replied with a number of possible sources.
There is a photo of the RBBB advance car in the red, white and blue livery in the book "Circus Trains" by C. P. Fox (Kalmbach, 1947), taken sometime between 1942 and 1947. The car was an older, wooden-framed car with truss rods, having been updated with metal sheathing and retrofitted with cast steel underframes. A second view of the same car is on page 89 of the Fox and Tom Parkinson book "The Circus Moves by Rail." It was converted into a laundry car when the hospital cars were acquired in 1947, and it's been preserved.
http://www.flickr.com/photos/27847413@N00/7867289870/It also was suggested that I contact the CHS librararian to gather additional info. At some point, I'll hunt down the Fox book.