Okay I got one here that is something I haven't seen before.
Kohler CV680-3016 2008.
When mowing engine sounds as it is flooding out. I try the fuel shut off valve and continues this until it runs out of fuel. #1 plug is black and #2 is only partially blacken. Compression is 180 #1 and 140 #2 so I would have #2 would have been causing. I have new ignition coils as it seem #1 wasn't firing all the time but that is not it.
Being a single barrel carburetor I don't think it is a carb issue. But while I putting the old coils back on I pull it and check.
Can it be that the engine is simply worn out and that #2 is causing the lost of HP when the deck is under load?
At least I now know the root cause of the deck being thrown and it is engine related even though one of the idler pulleys was bad.