In regards to the issues people say about the H2 vs the KZs they all really have fixes
Vibration; properly balanced crank and rubber mounted cases.
Handling; new swingarm bushings, upgraded brakes, proper fork oil and springs, new rear shocks.
Overly peaky power; port job and reed valves will increase bottom end power and peak speed.
Overall they are decent bikes and can be had cheap (mine was a 2 owner 3,000 mile bike, for $2 a cc... But it's torn down for pistons and crank seals) with a lot of digging.
my bikes; 80kz1000(project), 77 gl1000, 74 h2 (project)
Past; 78 kz1000, 83 kz550
Andrew
