What is the eye to eye length of the GSXR shock? The Gen2 1200 would have been 320 mm with a 61 mm stroke. The common shock transplant for the Gen2 B12 was a 1st Gen Busa Shock, which would have been 330 mm, and this would normally raise the rear about an inch (not really what you wanted).
I don't know the spring rate of the GSXR shock either. Maybe a bit more research is in order. The Gixxer is a much lighter bike, and your lowering link is providing more leverage as well, so making everything softer. You might need to add a stiffer spring to the Gixxer shock?