Yet another argument for wearing a helmet while throwing
If you look at the soft fabric throwbags typically used by tree climbers you'll see that the ring/eye is attached on the narrow end of the throwbag. This optimizes the the ability of the bag to slide through tight spots in the tree. You have the throwline attached at the center of the stone which will cause it wedge tight like a grapple hook when you try to pull the bag through a narrow space.
Another reason the weighted fabric throwbags are so popular is that the soft bag dampens ricochet when you're throwing. A hard throwing device tends to bounce much more when it hits a limb or branch.
The rock works but it will create problems for you. You can make a decent fabric throwbag with a short piece of tubular webbing filled with metal shot, you can sew or glue the ends.
-AJ