I would normally suggest a through bolt and cables also, but in this case it looks like the damage might be too great. The life of the tree is a thin layer of tissue under the bark called the cambium. On the broken piece it looks like less than 20% of the bark and cambium is intact. That might not be enough to support the growth of the tree. On the upright piece of the trunk there is only an inch or so of heart wood, which is the strenght of the tree, left. Another thing that may work against you is it's been several months since the damage occured. If it had been pulled back together, bolt installed, and cabled, within the first couple days, it would have had a better chance. Now the bends in the broken piece have had a chance to "stiffen up" so to say. When you try to pull them back together there can be more damage done by forcing the pieces back together.
It's a pretty little tree, but I think I'd start over. If you take the broken piece off there's not much strength left in the upright piece, and that's a big hole to fill in. Will your insurance help cover rerplacement?
On a second thought, you could also put props under the limbs to help support the weight of the crown, and take weight and stress off of the tree itself. The props would be under the canopy and out of sight. But, if it were mine, I'd still start over. Good luck, Joe.