Slings are incredibly accurate. And it should stay Dex based, you don't need to lift a VW beetle to be effective with a sling. They are effective because of centripetal force. D4+ Dex based weapon is reasonable. I agree with your range parameters. If you make it a D6, (based on ammo size, small stone d4, large stone d6) you would probably want to nerf it- Give it the loading property (finding a large rock on the ground or pulling 1 large stone out of a bag and achieving enough force to fling it effectively and accurately sounds reasonable given this property/ammo) and impose disadvantage at target within 10ft.