Someone had mentioned hand-eye courdination problems, so I thought I'd throw this in FWIW.
Take a sock ball or some such and suspend it (start with twine) about eye level in the center of a door way. Now you have a "two legged cat toy".   It seems to me that this same same striking/akido/kendo/jo trick to improve shot placement would also improve slinging.  I haven't worked out the details as far as using it for slinging as it just came to me. It does work for throwing things by hand as well as non-projectile strikes.
Prehaps making a "dummy sling",ie. two cords attached to another ball to act like a sling, would work... If nothing else it's an idea to mull over and play with.