What year is your 1150? I've got an 84 and an 85 and as far as I know there isn't a lowering kit available. Go to GS Resources and sign up on the forum, tons of great help for that old girl. I actually bought my 93 750 gixxer as a donor for one of my bikes but a bet from a friend resulted in reassembling it instead.
You can put a gsxr rear swingarm on, and a rear shock off an 07, when I mocked up the 750 arm on the 1150, I figured I was gonna drop about 3". A side benefit is you can run a wider tire and opens up a larger selection for brakes if you want something "bolt on."
I just do what the voices tell me.