Dude, it has a SIX GALLON GAS TANK!!! You know how much 6 gallons of gas weighs?
Ive accidentally dropped mine at a stand still. Same thing as you, foot hit some gravel/grease/oil and over she went. 515 pounds DRY can do that.... Every ZX11 rider here, except Squidge of course, :crackup has probably done the same thing. Buy some frame sliders like I did.
The bike isnt meant to be STANDING STILL.
Smaller wheels wont do it either, because its been proven that 16s are TOO SMALL and QUIRKY.
So I would suggest you be carefull with a handful of bike when at a stand still, or buy a different bike...
The ZX11 is NOT a "true" crotch rocket" per se due to its weight and size. It was meant to be a comfortable, long range bomber, that can hold its own in the twisties when it has to.
Want to lower it a bit, cut about an inch off the rear spring, and raise the forks in the tubes the same amount. That ought to also screw up the handling real good as well...