It seems I remember there was a time where number 2 had to be flipped upside down on some Kohler twins but that may be something I read several years ago so don't assume I remember things correctly. But it is worth a try.
As for the flywheel it shouldn't be a problem as there is only one trigger magnet set for both coils. If the engine runs fine on one coil and not the other it is something to with the coil mounting place.
I simply don't work on enough Kohler engines to be consider anywhere near an expert.
This from the service manual has always confused me maybe someone else can make sense of it.
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