X360 John Deere lawnmower issues

Might be fuel problems. If you done all that with no help, look into the fuel side.

Other common problem with those is the vent on your gas cap gets clogged, and without air getting in to replace the used gas, a vacuum is created that prevents fuel from getting to the carb. Try loosening your gas cap. You say it doesn't seem like a fuel starving issue, can you elaborate

There is a little electric solenoid on the bottom of the carb bowl labeled as an anti backfire shutoff. Make sure you hear it clicking when you turn the key on and off.
I just got done fighting my x300. Was trash in the needle for the bowl float fuel cutoff. Would let too much fuel into system and basically flood it to death. Also Kawasaki has problems with the intake manifold gaskets blowing out. While running spray starting fluid around both intake gaskets and see if engine speeds up.
My fuel filter is never full all the way. Usually only half. Hope this helps

Any help given is used and really appreciated. I thought about the fuel cap and have left cap loose all the time but issue still isn’t resolved. John Deere tech ran it today for over an hour and couldn’t find any issues. Could it be a wiring harness issue that when bouncing around a loose wire could be making it kill? Problem is that if this was the case, it would never start back up if the wiring is the problem. It’s like it’s overheated and this is why it doesn’t start up right away.

Had a John Deere mechanic give me a call. Told me he sees a large amount of sludge and trash at bottom of tank. Seems to think that me running it down to empty must be getting it to clog up. Will take tank down and clean it and change fuel lines, fuel filter and clean carburetor. If that doesn’t work, then it will be a new wiring harness.