So you have the 7000 series Kohler KT725 2 cylinder engine .
AFAIK this is not a specific model problem so I go back to the original suggestion to check the valve lash
Take the rocker covers & spark plugs out then turn the engine over by hand slowly .
Each valve should go in & out exactly the same amount
If they don't then you might have a cam wear problem
Set the valves to 0.004" and see if the problem goes away.