Hi and thank you for your question.
I am happy to help you resolve the problem with your Jet Ski. I do however have a couple of questions for you that will help me more fully understand what you are up against.
First, why did the cylinders, pistons and rings get replaced? Please be as detailed as possible.
Were the parts replaced with OEM Kawasaki parts or aftermarket parts for a Kawasaki?
Who replaced the parts?
Is a gas diverter valve also known as a petcock, or as Kawasaki calls it in their parts diagrams a fuel tap assembly? Why was it replaced?
As far as the stator, it is very difficult to measure less than 1 ohm resistance so I wouldn't worry about that. It sounds like you have good AC output on the stator leads so that should not be an issue. Even if it were, it would manifest itself as being a dead battery. The ignition system is a magneto system that does not use the battery for running. The battery's main purpose is powering the electric starter.
Unless you have already confirmed it, I suggest putting an automotive style inductive timing light on one of the spark plug leads and put the pump in the water and see if you are losing spark at half throttle. If the engine goes into a mis-fire, or does what ever it does preventing it from revving up, and the spark remains constant, you do not have an ignition/electrical problem. If the ski is on a trailer, you don't have to take it off the trailer for this. Just back it into the water still strapped to the trailer and do the test right there.
If you are not losing spark, the next thing I would like you to do is a compression test on all 3 cylinders. I fully understand those parts are new but we know we have a problem with the ski so we don't want to assume anything. Make sure when you do the compression test you leave the 2 spark plugs installed in the cylinders that are not being tested. Ground the high tension leads to a suitable ground. You do not want to actually run the engine while performing the compression test.
Lastly, I would suspect a fuel supply issue, quite possibly carb related. That however is the last thing I would suspect and definitely do not advise going into the carbs until we address the other points first.
Let me know what you find,