The problem turned out to be that the porous bushing on the speedometer's input shaft had dried out. The input drive on the speedo would work for a while, then the input spindle would overheat and seize, breaking the cable.
I'm thinking you've hit what's wrong with mine. I finally got the speedo out of the dash today, the cable end of the drive will not tunr bt hand, and the drill strains a bit to get it going. I'm going to pull it apart to see what's going on. I have priced new speedos just in case.