Well, I haven't been much help to this point.
Again, you might check the eyelet on the ECU ground wire. Kohler had an issue with corrosion, not where the eyelet contacted the engine but where the wire made contact inside the eyelet. You might just look at it and see if there are any signs of corrosion.
The fix was to cut off the eyelet and solder on a new one. The factory one was crimped but in the field crimping often doesn't work. It needs to be soldered. A faulty ECU ground could cause the issue you're having.
If all else fails, you might call Kohler's tech support line. They take consumer calls these days although I think their best Bosch EFI guy has recently retired. I believe their tech line number is 1-866GOKOHLER.