Wow, I am suprised the FJR is so fast! I guess I better not try a pull on one of those guys, might get spanked.
Anyway, for the OP, make sure you have fully 'outgrown' the FZ6R before moving up, likely around 10,000 miles or a year, whichever comes first. Then you can pretty much move to any bike you like, for serious 2-up you can forget about the SS bikes, so that puts you on sport touring (ST) bike, but ST bikes are heavier. You will just have to decide how important 2-up riding is to you, its kind of selfish to make a passenger suffer, the FZ-1 might be a good split between the two. I know my wife really isn't that interested in being a passenger, so I get to choose whatever bike I want, so I am staying with lightweight SS's for now - but if your girl wants to participate, then try and make it comfortable for her, there will be trade off's on the sport end, though.
Ninja 1000 is prolly a really great choice as well, but yeah, insurance may suck due to the 'Ninja' name, but just pay it and get the right bike.