If you must use the factory Kohler supplied pump, then I would use a .020" or .025" copper MIG welder tip for my orifice. You could make it even smaller by adding a piece of steel guitar string ( .008", .011", etc etc. ).
Of course...., you could always use a car power steering pump (or very small hydraulic pump) that is belt driven and have a 100% full flow system drawing oil from the crankcase drain, filtering it through a Fram XG8A, and then returning to the crankcase (a non pressurized system).