Without looking at your system, I suspect that when all the switches are closed a ground circuit is completed.
Trace a safety switch wire back to the dash, there should be a second wire coming into the dash that runs to a relay from the safety switch circuit.
Those two wire need to be cut and spliced together.
You could also run those two wires to a N/O momentary switch that you mount to the dash to create your own safety switch. IOWs you will have to push the button of the new switch at the same time you turn the key to start......that will keep kids or others from starting the tractor......will also force you to look around and be aware when you start it.
Another way to do it.....
With a test light, there will be 5 or 6 wires attached to the back of the ignition switch. With the test light, determine which post is energized when the key is turned to the START position, that post will only be energized when in start.....serves no other function, remove that wire. From that post run a new wire directly to the trigger post on the starter solenoid.....you have now bypassed the safety circuit and created a new circuit.