I figure you knew that the coil was bad after testing the coil's resistances so I didn't look up the actual wiring of that engine. But since I have, did you replace the ignitor module [PN 21119-2161]? If not then it is likely to root cause and it should available in aftermarket or you could the universal version that Stens has under PN 440-465. But also make sure the kill circuit isn't grounding out the ignitor when it is not in shut down mode.
Ignitors [electronic triggers] are more prone to be bad than coils. It is the same with coils with built-in ignitors. It just they are not replaceable in those coils.
Kawasaki FC290 Service Manual
PDF page 42 has the resistance checks for the ignition system. Just note the ignitor resistance checks don't cover every failure.
As a side note I had one these ignitors to fail once where it would randomly misfire on compression stroke and when the wasted spark worked nearly sat my pants leg on fire [about a 12" flame thrower] and sounded like my .357 going off.
