Hello Monty72,
The X300 series was a new model back when I was a JD service manager for a local dealership. These are great mowers that were well built.
A key point to remember is the pulse style fuel pump on these and similar mowers is a "flutter valve" mechanism and it only pumps (transfers) fuel as the carburetor needs it. These are not mechanical gear driven pressure pumps. they are operated by the internal engine pulses of the crankcase as the piston(s) move (back and forth) in the cylinders.
To test the fuel pump, disconnect the line at the carburetor and place the line end in a jar or cup to catch fuel. Crank the engine and see if it steadily pulses fuel as the engine cranks. If it does, there is not a pump problem.
If it just "spits" a little fuel and delays, start by checking the pulse line from the engine for cracking or splitting. Next, check all the fuel line connections for cracking or splitting near the clamps. Fuel lines get old and rigid with time. Back at the rear of these mowers is where the fuel line connects if I recall correctly. Look for any cracks in the line there.
I just had a Cub Cadet Z-force 48 that dry cracked the fuel line at the fuel pickup fitting. It was sucking air instead of fuel to the pump.
The same conditions you described were happening.
With your X300, it can very easily have debris in the tank that is blocking the fuel exit nipple. Also, the inner gas cap seals were bad about breaking apart and the rubber chunks would fall into the tank and block the fuel exit nipple. This may require that the rear platform be removed to access the tank and remove it for a good cleaning.
If the pulse pump cannot get free flowing fuel, it cannot pump/transfer it to the carburetor.
Hope this helps you.
