About 45 years ago I knew these transmissions well and have probably rebuilt hundreds of them. But that was then. Now I sometimes struggle to remember what I had for lunch yesterday.
You didn't provide a lot of details about when the problem started. Was the car fine one day and the problem presented itself the next? Any recent work done before the problem presented itself? Sounds basic, but did you check the fluid level? This should be done with the car warmed up, sitting on level ground and the engine running and transmission in Park. What does the fluid look like? It should be a transparent Red and no burnt smell. Brown and sludgy is not good. Usually if the fluid is low the car may be hesitant to move and may not upshift. If the fluid is mucky it could cause valves to hang up and the transmission not shift properly.
As mentioned before the governor and vacuum modulator send signals to the valve body that it uses to determine shift points. The vacuum modulator provides throttle pressure and engine load input. The governor provides vehicle speed information. It is very unusual for a car to shift into high gear by 10 MPH. It is not likely a governor weight or spring problem, but a slight possibility the governor valve hung up.
As far as simple fixes maybe the modulator valve hung up or modulator could be bad. One thing worth trying is removing the vacuum from the modulator. The steel line from the modulator runs up the transmission to a T fitting on the rear of the carburetor. Disconnect the steel line from the T and plug it off at the carb end. If there is no vacuum going to the modulator it would essentially tell the valve body you have your foot to the floor and cause it to raise the shift points to a higher speed. If no change you could remove the modulator and see if the valve is stuck in the case (use a thin nose pliers). With the modulator removed turn the vacuum end towards the ground. If oil comes out the rubber diaphragm has ruptured, and the modulator is bad.
One thing worth mentioning it is not easy to remove the governor with the transmission in the car. Especially on older cars the steel cover tends to corrode and stick to the aluminum transmission case. Sometimes it is necessary to remove the cross member and drop the rear of the transmission down a little. After the spring retaining clip has been removed you have to work arround the cover with a large straight blade screwdriver, not easy to do in a tight area.
