I would use two bodies (with a 15-85 and 100-400 presumably) before I would decide to carry a single bazooka lens (and a lens that does 560mm at the long end cannot be anything else, especially at f/5.6 aperture). YMMV. Actually I've done dual wield with a 16-35 and 70-200 and it's a great thing to do, very comfortable and adds a degree of failsafe.
(I've noticed that you're at exactly 1300 posts and I'm exactly at 900 now. LOL)
(I've noticed that you're at exactly 1300 posts and I'm exactly at 900 now. LOL)