I'm not an expert by any means, but most mechanical speedometers (with actual speedo cables) work on the following priciple. The cable connects to a magnetic disk. As the disk spins faster and faster it pulls a corresponding (but not connected) disk against spring tension. The indicator needle is connect to this second disk. Sounds to me like the problem is really in the speedo head.

But, I'd try lubing the cable first. When that doesn't work, find yourself a speedometer shop. There are still some left. Imagaine you can find one in the Yellow Pages, asking at vintage car restoration places or maybe a local repair shop, looking in Hemmings Motor New or on the Internet. They can clean and calibrate it for you.