Very nice writeup and pictures!
For troubleshooting, a condensed version would be faster than going through all of that, and rule out other problems that cause the same symptoms as a bad solenoid, i.e.:
1. Verify solenoid is grounded through mounting tabs with multimeter on lowest 'ohms' setting- check for zero resistance between solenoid mounting tab and - terminal of battery. If OK, then proceed to step 2.
2. Use voltage setting on multimeter to ensure there is 12V at the small wire going to the solenoid when the key switch is in the 'start' position. If OK, proceed to step 3.
3. Momentarily connect two large solenoid terminals together with large screwdriver, pliers, etc. taking care not to accidentally touch anything grounded to the chassis in the process. Starter should engage.
If steps 1 and 2 are completed successfully, and the tractor spins over when step 3 is performed, the solenoid is bad. That's all there is to it.
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