Did you pull the clutch plates out and inspect them? They may be stuck together and need to be cleaned up from setting. They get gummy and rusty plates from old oil left in the motor over many years. At 16,000 miles the clutch shouldn't be worn out. Beadblast/vaporhone the steel plates and clean the clutch discs, then lightly sand them to refresh them(keep in order and direction when you pull them out)
Yes a proper adjustment at the actuator lever nut behind the clutch chrome decorative plate is necessary per the service manual, then at the clutch lever.
The other thing to check after you make sure that the discs and plates are not gummed together is behind the transmission cover (left side, that has the shift shaft rearward of the alternator cover, you will need a new cover gasket to do this), the large Allenhead screw holding the shifter hook might be loose. When Sean(The Lone Builder/Belfast to Belfast/2) stayed at my place back in May this year, he had a problem of his K2 from Ireland that he bought new not shifting to neutral that adjustments and checking the clutch pack didn't correct. Talking with HondaMan, he mentioned having found the large screw loose on more than one bike he had repaired.
Report back what you find here.