Not sure where you got the sub 500 pound wet weight for the VFR800. Pulling wet weights from Total Motorcycle shows the VFR800 at 551 wet, the K1300S at 560 wet and the Sprint ST at 530 wet.
I've have a K1300S and rode a 99 VFR800 for five years. The VFR was a great bike but the K13S doesn't feel any heavier and has gobs more power and a much better suspension. BMW weird, I know, but it works very well on the road. A chain wouldn't keep me from buying a bike I want but I do not miss chain maintenance. Riding position between the VFR800 and the K1300S are almost identical. I thought it was interesting that I found the VFR1200 to be a little tighter, more like the Sprint ST.
I spent a year with an FJR1300 too. Nice bike, very capable, easy to work on and dead reliable. Too much bike for me though as I never got it out unless I was going out for the full day. Just seemed too big/heavy for a local ride.
You might consider the Ninja 1000 too.