Shifter problems
One other thing you might want to consider is how many thousands of times that old gearbox has been stirred by that little chrome stick. There are several places in the linkage that wear and this causes your lever to have to move greater disances all the time before something happens.
The shift arms on the trans, linkage rods, clevises, and the various parts of the shifter itself can become worn to the point of not being able to be adjusted properly anymore. I would recomend removing the shifter, disassembling it, and replaceing anything that looks worn or bent. There is a shim in the shifter, called a shifter interlock, that is located between the levers that is a common wear item. Replace it when you have the unit apart.
After this and properly resinstalling and adjusting the shifter you should once again have a happy 4-speed. You can find the items you need in the Paragon catalog,
www.corvette-paragon.com . No I'm not on their payroll, it's just that they have the right pieces. Others may also but this is the place I'm familiar with.
They also sell a complete repro shifter if yours is too far gone to rebuild. And, if you would rather have a Hurst shifter but don't want to give up the original appearance, they have an original style lever for the Hurst that will make it look unmodified from inside the car.
Tom