Based on the combination problems involving the coil kill wire and the PTO activation, I would suspect the PTO switch is bad.
I do not have a schematic for the 300x, however I most of the functions are comparable to the LA 145, 165, 175.
The PTO switch is a multifunction switch. It will have 3 to 4 different functions internally. On the LA 175 it serves 3 functions. These 3 internal functions are independent of one another. Electronically they are known as single pole/single throw switches. In other words even though they are all housed inside a single unit they act light 3 separate light switches in your house.
One function ("light switch") controls your cranking system. When the key is turned to Start, power flows from the Key switch (purple wire) to the PTO switch. With the PTO switch off it flow out (purple/white) and goes to the Brake switch. If the Brake is set the power flows through to the starter solenoid and your engine cranks.
Another "light switch" inside the PTO switch controls the Blade Clutch. Power flows from the Key switch, in run position, (yellow wire) to the PTO switch. With the PTO switch on it flows out another yellow wire to the Blade Clutch. A DC volt meter should show 12 volts switching on and off as the PTO is turned on and off.
The third "light switch" completes a Ground Path. This ground path is a totally separate pathway running through the PTO switch. The ground system is fairly complex because it operates differently under different scenarios.
To produce a spark, the key switch must be in the start or run position. While starting the PTO must be off and the brake set. The seat switch does not matter at this point.
Once the engine is running the seat switch plays a part if the PTO is activated or the Brake is released. Someone must be in the seat.
The Kill system is activated
- When the key switch is turned off.
- When the operator leaves the seat without setting the brake and turning off the PTO.
- When the machine is reversed while the PTO is engaged and the back up switch (RIS) is not pressed.
So there are three different paths to ground; any of which can kill the engine by grounding the coil. Except for turning off the key, all other grounding functions flow through the "grounding light switch" in the PTO.
Because you have a combination problem, the Coil kill wire is grounding the engine and the Blade Clutch won't activate the blades; both of which are affected by the PTO switch, odds are you have a bad PTO.
Obviously there are too many complex functions to just bypass the switch. You will have to replace it. The part number you need is AM135131. You can do a site search to locate and order this replacement switch for about $26.00 including shipping at this site: GreenPartStore Parts for John Deere Lawn Tractors John Deere Lawn Garden...