You could try this to see if the solenoid is working. Leave the tractor in "gear" so it won't crank over. Turn the ignition switch to start (but it won't crank over because of the interlock). Turn the key off and you should hear the click from the solenoid. Every time you turn the ignition on/off, it should click. Several seconds after turning off you should also hear a click (my GC2300 is 8-10 seconds). Is it possible that a relay isn't working properly for the shutdown? The parts are too expensive to just replace en masse. thepumpguysc seems very knowledgeable, maybe he can recommend a methodical way of testing each component.
I just went out and tried what you told me to try, I heard both clicks you speak of. I am wondering if I somehow reset that replay during my diagnostic work today? Could be that is what wasn't working. I wish I knew where it was located to make sure the contacts look good.