Sorry for the delay everybody. Apparently I need to change my notifications so I know when somebody has replied to me! The problem hasn't been resolved, but I have figured it out a bit more. The fuel shutoff solenoid is not getting power while the starter is cranking, but gets power when the key is on or the tractor is running. I rigged up a test light so I could see what it's doing. In the warm weather, it's been working to just crank it a few times and as soon as I let off of the key, the solenoid opens and the tractor starts up. A mechanic friend of mine said that often the circuit supplying voltage to that solenoid during cranking is a completely different circuit than while it's running, so figuring out where the problem is could be tricky. But he's not a tractor mechanic, so who knows if he's right. One day I need to get out the wiring diagram and trace the whole starting circuit to see what might be the problem. Hopefully just a simple relay.