Wiring is real simple on this unit
White originates from the starter, it's NOT the white/black, it's a completely separate connection and goes directly unfused to the solenoid.
That part of the circuit is working as the tractor will start but as soon as you let off the starter it dies.
The black is a simple ground, it's also working as it will start.
What's not working is the red wire circuit, that is the hold circuit, it's powered buy a timer relay or more likely just a jumper that or standard relay that gets it's power from the switch via a 15 amp fuse.
There is no 5 amp fuse as that is used in models with OPC setups.
If your getting power to the fuel pump then the issue is in the fuse or wiring between the fuse and the solenoid.
The reason you burned up thee solenoid is that you powered the white pull in section of the solenoid and that should only get power momentarily while cranking, the red gets power all the time to hold it after pull in.