67 Barracuda rallye speedometer issue

The part that people miss is the hardened grease/crud build up inside that square drive port. The cable is supposed to slip fit and not put any pressure on the instrument in any direction. The collector nut that your model has never did provide enough cable support and alignment so that nut was changed to a plastic sleeve about 1.5 inches long in 68 and later. All you can do is clean the input port, route the cable in straight as possible, snug that nut and cross your fingers. If your disturbing this worn fitment amplified and showed you the wear that was already in the instrument, you could pay about 200 for restore, or buy a good used 68 or later speedometer without the trip clock and buy a new cable for that 68 and later model. I wont detail the additional problems that the trip clock causes. I will add a tip...
When we see a picture of a speedometer for sale, it is resting or propped on its input/spindle. If that pressure lifts the needle farther than 7 mph, let them keep it, shop for one that shows less wear. Wear in the bore lets the magnet shift off center, that lifts the needle. When they were new, bias pressure on the spindle didn't lift the needle at all.