Yes. Check the brass link joining the upper and lower shift rods. One or both has not been fully inserted in the link. Access would be under the port on the side of the leg.
You describe the old-style cable with the two set screws that together grip the inner cable wire. If your fix fails, you can still find the older style cables, if in fact that is what you need.
As you probably know, reversing battery wires for a split second will blow out the rectifier, as would disconnecting the battery while the engine is running. Don't give up on old Bill from Occam.
Maybe this, at the address Crosbyman suggests. The old-style OB gauges had a sensor and bracket for physical contact with the top of the powerhead (think this one would work that way too)...
