possibly starter issue
kohler updated the starter a few years ago, it's about 45% more powerful now, the shaft is larger as well. Often the old style ones (if yours is original it's probably the old style) would fail, magnets come loose inside, shaft bushing wear out/break, sometimes the gear/shaft would just break completely off. Really a crap design and another reason I don't really like Kohler. If you order a chincanese starter, it follows the original (weak) design in most cases. I highly suggest replacing with a Kohler brand starter if possible. Yes it costs a bit more but these newer ones don't fail much. Another thought. Perhaps an engine issue? How's the oil level look? Is the end of the dipstick burned/brown? And, I've seen one or two PTO clutches fail and cause hard starting as well. Last thought, for what it's worth, is ground. If the engine ground isn't good, it won't turn over very well. You can test this with a volt meter, one probe on the - battery terminal the other probe on the engine block. With someone cranking the engine while you watch the volt meter, you should not see more than about 0.5 to 1.0v diplayed on your meter. If it's higher, check the ground wire connection.