I've seen other bear sacks that instead of tying to a 5" limb or bigger, they used a cable to secure to a tree trunk.
If you rather not hang a bear sack, but think like I do that finding, that perfect limb MIGHT be a problem, I think quick trip to the hardware store could fix that "potential" problem.

Buy about 4-5 ft of that steel cable with the nylon coating, the type you see on garage doors.
It's plenty strong. Have the hardware double crimp loops on each end. Then find a locking type of carabineer, maybe for hardware or sporting good store.
Loop around tree, secure with carabineer and then tie sack off as directed. I think it would be just a secure and easier to deploy just about anywhere you have trees.