Depending on some other factors, the first thing I would check is the auto compression relief aid for starting. The compression reliefs on Kohlers, in my experience, act up in cooler weather and will cause the intermittent problem you are experiencing. There should be a check valve with a detent and spring that can be removed and cleaned. Older motors with a bunch of hours can build carbon deposits and newer motors that do not have frequent service can illicit these same symptoms.
The key to this is a slow, steady pull, allows the engine to crank enough to start.
One other thing, call Kohler, speak to a technical person. Kohler has people that exist to answer questions solely to commercial users of their equipment.
At one point, I maintained over 150 acres of golf course and park settings and in my equipment inventory I had something like eight Kohler motors. During my winter service time, I purposely checked the compression relief systems, and in the spring, bingo, no more hard starting or the opposite, no compression, fast spin no run situation.