Make sure that the fuel tank is vented. Next time the engine stalls, slowly remove the gas cap. If you hear a hissing sound, you have found the problem. Sometimes the gasket on the cap will cover the small indentation at the top of the tank filler neck which serves as the tank vent. You will have to look closely, but the indentation looks like someone placed a small dent in the filler neck, but that is the vent.
The Ford factory service manual explains the installation of the ring and pinion. Some gear sets are lapped in a particular way that the gears must be installed in time with one another. The gear teeth will be marked with paint and have to be installed with these marks mating. If they aren't installed correctly and in time you'll never get them to quiet down.
Some gear sets will always be noisey to a slight degree, but it shouldn't be excessive. Some sets will quiet down only a little after a short period of run in, but if the pattern isn't right and the gears aren't in time, forget it. Most gear sets will have a break in procedure that must be followed also. If it's a used set of gears, then following the service manual would be the best way to go.
Don't use gears made for racing on a street car. They are made of a softer metal and will not last. | 
