I have been riding an 89 Ninja 600R for the last 4 years and like it so much, I deceided to keep it instead of buying a new bike this year. (I have been contemplating a new Ducati)
I do not mean to offend, but you do realize that there are two adjustments for the stock rear shock don't you?
The first is the air pressure (preload). There is an air valve under the right side cover. I am 6 feet tall and weigh 195 and run at zero. To get it to zero put the bike on the center stand and depress the valve to allow built up, or negative pressure (occurs when sitting on side stand for a long period of time) to release. If you decide to add air, DO NOT use compressed air from a tank! You will blow the seals! Use a GOOD manual bycycle pump with a gauge inline or take it to your local Kawasaki dealer and pay the $40 or so to get it set up right. The manual says max is 70 psi. I would not exceed 30 or 40 psi if It were my bike. I think you will probably use 0-20psi for your situation.
The second adjustment is Damping force. This is done by changing the position of the adjusting stick also under the right side cover. There is a small black knob on the end of the adjuster. Fully pushed in (position 1) is the softest setting. All the way out (position 4) is the Harshest. I run at 3.
I run Avon Super Venoms front and rear and have no complaints.
Best of luck.