I had the same problem with my 54 (3100). I ordered 3 sets of cables before I ordered the correct cables from "Inline Tube". The first 2 sets came from Classic parts and Rockauto. They were both the same with frame connection not anywhere close to the original. The 3rd set came from Rockauto again, but this time a Dorman product. The frame end looked the same in a picture, however, too large in diameter to go into the frame bracket. And YES the frame bracket is cast and you will brake it if you try opening it up. The ones from Inline tube are an exact replacement, however they are more than twice the price. You can also order them in stainless for even more $$$. I have to throw this in... During the restoration of my 54 3100, finding parts has not been a problem, finding good quality parts is a BIG problem.
Big names like Bendix, AC Delco and Dorman all package the same overseas junk. I just have a hard time understanding why they don't check the quality and fit before they package in their boxes. Frustrating some times!