Welcome to the bum ignition switch club! The key cylinder and switch are separate components and the fix you require is not that hard. When you start your car the ignition switch sends power to the starter and the coil. When the car is started, the running position of the switch continues to send power to the coil to keep the engine running. In your case, wear inside the electrical half of the switch is failing to do this. The part you need is VWC-311-905-865-A available from CIP1 for about $25.00 (US). Yours is the older style which comes with wiring which you will have to match and join. Olspeed's instructions will remove the steering wheel etc. It really is easier than it sounds. Once this is done you shouldn't need to replace the key portion of the assembly. While you are waiting for the part to arrive, you could run a hot wire from the battery to the place on the coil which receives the power. Break the wire with an off-on toggle switch. Switch on when you need to run; switch off when you are done. Good luck with the fix and welcome to the forum. Dan (MY72BUG) in Goderich, Ont.
I'd rather have a partial bottle in front of me than a partial frontal lobotomy.