Ignition just cuts out.

It sounds like a possible ignition switch problem. Check the voltage at the coil positive teminal while cranking there should be 12 volts while cranking and about 10 volts after you let off of the key. There are 2 different contacts inside of the ignition switch, one that sends a full 12 volts to the coil positive teminal while cranking and another that sends the 12 volts to the balast resistor to lower the voltage after you let off of the key so you don't fry the points. It seems like when you crank the car the one pair of contacts are bad and when you let off of the key the second contacts are appying the voltage so it tries to start. A volt meter on the + side of the coil will answer the question.

Good Luck!