I have seen a couple of mods for the restricted intake on the Z1000, but this is how I did mine. The photos are with the original filter so it is easier to recognise. I am now using a K&N filter.
1. Take the lid off the airbox.
2. I have used some aluminium strap which is 10mm wide which you can buy from Bunnings. One end is pushed into the airbox lid location slot at the front.
3. I have used aluminium angle and the original screws at the back of the airbox.
4. Make a bend in the strap at the angle end so it will apply pressure when the angle is screwed down.
There you have it a very simple and effective mod, no need for the lid therefore no modifying the original lid, so you can put it back on when you want to sell the bike.
I have been using my bike like this now for about a month with no problems. The only side effect is a loud growl when you crack open the throttle.....mmmmmm sounds sweet.