It looks like you have the infamous "Huck" brake system- - - -which works one of two ways- - - -poorly, or not at all. In around 1951 Chevy swapped over to Bendix brakes, which work a lot better, and were used by various manufacturers other than GM. One approach would be to find a donor vehicle and convert to Bendix brakes- - - -drums, backing plates, shoes, and all the hardware. "Buy once- - - -cry once!" There are a lot of sneaky little tricks to making Hucks work, like sanding the linings to the exact radius of the drums, and/or making frequent adjustments, but you'll need to acquire all the right parts to begin with. Be patient, follow the service manual procedures to the letter, and don't take any shortcuts. Good luck!
Jerry