If you start it up and leave it at idle does it keep running rough or will it straighten out in a while. Observe the throttle shaft while it is running rough and when it smooth, is it in the same position, is the position steady. It could be the carburetor idle circuit/adjustment is not right causing the pour idling then when you increase the RPM the high speed circuit takes over and it smooths out. Most of the equipment I own has trapped air in the fuel filter. so long as there is fuel coming out of the fuel line at the carburetor it makes no difference. All the engine cares is it gets fuel. I forgot to ask have you checked the manuals section (third tab from the left top of this page) You may find an engine manual there with trouble shooting instructions, John Deere is very protective of their manuals so you will not find a tractor manual there. If both plugs are firing consistently. You have only fuel air mixture, compression and timing left to check Don
I will have to work on this again tomorrow as it’s 9:45 here now and I don’t want to annoy the neighbors! My fear is possibly compression. I do not have a compression tester yet (possibly pickin one up this weekend). I was able to download an onan manual for the engine. As for the air fuel mixture, considering this engine is a ‘99, I have to assume it has the non-adjustable carb. Now timing, what are the steps to checking that?