Well it appears we may indeed have an ignition fault with the Kawasaki afterall.
He drained and removed the tank, everything looked somewhat normal. No critters in the airbox. There is one small diameter vacuum hose coming up from under the carbs and we couldn't see where it's connected at that end, but it went nowhere. Both lines going to the fuel tank were fine. When he pulled off the small side covers he found a mess. Someone has cut into the wiring harness and there's some poorly executed crimp-on connectors. I sense a short somewhere.
This could explain why the loss of power and seeming misfire is intermittent. Fuel supply related problems usually occur more consistently. He pulled the spark plugs and found two of the four were wet, and he did describe a backfire. That all points to ignition problems. He's trying to find a wiring diagram and perhaps photos of what the original wiring loom should look like.