Mine shifts fine but one thing I've noticed which was the same on the FZ6 Fazer I had a couple of years back, was the lever seems to have a long throw, and it needs to be allowed to centre when a gear is selected, before it will allow you to go for another gear. I've never had this problem with...
Just an idea
As the FZ6R has different names in other countries, searching ebay using European names may come up with (will come up with) a few more choices of screen. In the Uk it's called the XJ6, XJ6 S, XJ600F and Diversion.
Here's one I picked at random, I can't verify how effective it...