Apache Accuracy
Most of my accuracy experience is with Apache throws.
Slinging varied stone sizes, I have found a great accuracy gain from "feeling" the weight of the throw in my shoulder.
I am not sure if I can explain this, or if it might be applicable to other throw styles, but here's a try:
Instead of using deltoid, pectoral, and bicep muscles to throw, turn and move your body so that your shoulder moves in a straight line towards the target.
Do not twist in one rapid, jerky movement: that will give you no feedback on where the stone is and what it's doing.
Instead, start slow and then accelerate your shoulder towards the target. You will be able to feel the forces in your shoulder. If you do this right, your outstretched arm will accelerate at the same rate as the sling, and your arm and sling will always form one continuous line.
Your body has a great sense of where your limbs are at any given time, and you can train yourself (subconsciously) to release when your arm is at angle "x". If you do this right, then the sling will also be at angle "x" when you release. In theory, this should improve accuracy.
The slow start and progressive acceleration do not mean your throws will remain slow or weak. With practice, you can increase the acceleration in your arm and sling equally. The idea is to avoid using your arm as a staff sling or trebuchet, rather to make your arm be part of the sling.
Personally, I find this to be the most natural and intuitive way to sling accurately. While I get better power out of figure-8 and related side releases, I have a harder time judging release timing from the angles of both shoulder and elbow joints. With those throws, I also do not get a good feel of how fast the sling is moving, and so I cannot rely on my muscle memory to judge how heavy the stone is - leading to a more involved subconscious calculation involving my memory of how heavy the stone was when I picked it up.
I am sure that those throws can be just as accurate, but they may require extra practice and may gather greater benefit from uniform ammo.
Perhaps slingers with lots of practice with baseball, tennis, and similar throws already have the elbow & shoulder muscle memory learned, in which case it may be more natural using a figure-8 throw. Unfortunately, I used to play basketball
-pancaker