On my ZX-14 (very similar to ZX-12R, chassis-wise) the stock fork height is 3/4" above the top clamp to the fork cap/tube junction line. I have mine set at 1 1/4" (1/2" higher than stock) lowering the front end by 1/2"
This makes initial turn-in easier and does not affect stability as far as I can tell. I have also been running a /55 rear tire, which is 5mm taller than the stock /50 and this also helps the big whale flop into a turn and hold a line easier when accelerating out of a turn because it negates the tendency to stand up under power.
No clue as to some sort of "spacer" under the rear shock since the bottom mount is an "eye" and the top mount is a clevis, but adjustable suspension links or a shock with a ride-height adjustment could also alter the steering geometry.
My advice; baby steps. If you are going to change anything, change one thing at a time and see if you can tell a difference before you change anything else.
It may be a pig, but it's a pig with a rocket in it's ass!