I, too, hate having a sore shoulder from repeatedly attempting to throw a fair-sized rock again and again.
"However - if you must hang, you need to learn to sling your rock up into the tree. Which means using a rock sack,and swinging the rope around in a circle to get up momentum, and then releasing at the right moment and angle so that the rock goes where you want it to. It will take a lot of practice, but it will allow you to get the rock higher than you can throw it."
Yup, that's the ticket. Imagine Ayla from Clan of the Cave Bear, whipping a stone in a sling around her head before accurately casting it to dispatch a hyena or scare off a cave lion (backpackers were tougher back then!). Then turn that whole assembly 90 degrees - not a horizontal circle but a vertical one.
The bigger the circle, the more energy you've pumped into the rock bag and the further it will fly - way too far is easy to do. To allow a bigger circle, you can stand on a flat log or boulder to get a few more feet off the ground.
Rock bags (versus a cord around a rock) are especially good for the sling technical. Because the rock gets traveling FAST and if it comes loose, it could veer off and hit someone or go straight up and put yourself at risk.
You can lay our the extra line towards the target tree so it doesn't get tangled as you release the rock.
Try this at home only if you have a very large yard. Otherwise, find an empty field or park.
You've a got a kid along? Make a game of it. Put a target up in a tree at home and have the kids compete to see who can hit it first / most often / hardest. Then they'll have the timing and rock speed to arc over the desired branch. They also be all sighted in, should there be a bear on that branch late at night. THAT'S when I really throw my arm out - throwing heavy rocks as hard as I can at the bear.