Youre right about the "kill a pred" thread - best left for elsewhere. Suffice it to say you should rid yourself of those preds you can.
We never said all this was easy; responsibility comes on many levels when you take in livestock animals.
Hawks interest me. They don't saunter up, tip their hat as they open the gate and grab your chickens. No, they fly in fast, on the swoop and nail them broadside. So, that's the trick: defeat them on the wing.
Give lots of shelter for the cluckers to duck beneath and block the primary flight paths with approach barriers like tall plants and dangly-sparkly things. Then you will have done about as much as you can. 
My sister had a problem with hawks snagging her Austrolorps, which were being kept in a large, open pen. So we put our heads together and came up with a plan. She moved the Alorps to a sheltered area, then scattered plywood "tepees" and brush piles around the chicken paddock. The hawks still tried, but their success rate fell dramatically. The "Lorps liked the brush pile and shelters, too. I know mine love them.
Along with shoring up the fences, you should also think about electric wires along the existing fence at strategic heights. Not terribly expensive, they do a lot to deter "nosy" preds like foxes, coyotes and dogs/cats. I dont know if they'll work on bears!
All in all, it's best not to let chickens wander aimlessly in the open, but to control their movements in cordoned areas and give them overhead shelter. If you remember thier jungle roots and try to duplicate that, it eliminates a lot of worry. 
How does that sound?