I was unable to find any photographs at the time showing the appearance of an original Philco B-537 back. Instead I decided to make one along the lines of a Philco 444 back, adding the different openings and cut-outs necessary for the C-537 chassis.
Using images of the 444 back as a guide, along with a tracing of the opening of the bakelite case, I eventually achieved a full-sized paper drilling template.
Obtaining some 3/16 inch thick MDF-board, I transferred the cut-out lines and drill points over to it using the template.
After some careful cutting with an electric jigsaw and a total of 690 drilled holes later, I had produced the completed back-board ready for painting.