Dave,
A 77 rabbit is a wonderful thing (round headlights)- Sorry, Bill is right, the close ratio gearbox is a no -no, but you can use the fuel injection. I believe the 83 - 84 GTI have the same small throttle body, but the golf GTI throttle bodies are bigger. I'm sure there are some exceptions. In general, the fuel injection parts for that car are easy to get. The 76,77 and 80 car are all legal and many of the other rabbit/jetta years will work. Be careful when you switch back
the fuel pressure will need to increase and you may find your accumulator is missing in the car. If you need parts, you could call D & D Auto repair 870-289-7471. they ususally have good used parts you could buy at reasonable prices and they will know what the correct pieces are for that car.
Again, congratulations on the car