I hope nobody minds if I summarize my thoughts after reading this thread and rooting around a bit.
I note that in fact, the most aerodynamic shape is the tear-drop / rain-drop / pear-shape which Jaegoor was asking me about a few weeks ago.
https://www.quora.com/Why-is-a-tear-drop-shape-more-aerodynamic-with-a-round-hea...https://www.reddit.com/r/askscience/comments/21rz0tInterestingly, one issue here is one of frontal drag: a point generates more drag than a smooth rounded end. Some sling bullets in fact do have very rounded, egg-like extremities (others, on the other hand, have super pointed extremities-- esp. in ancient Spain, perhaps on the instinctive idea that the bullet "pierce" the air in flight).
I assume that having the rear end of a sling bullet tapering is the same principle as a boat-tailed bullet-- in reduces drag in flight.
So perhaps the most aerodynamic sling bullet would be a tear drop (round nose, long sharp tail; the problem is that the asymmetrical shape would not facilitate clean release. So the next best shape is "football shaped", but with rounded extremities to reduce drag (rather than sharp points): it is aerodynamically efficient but also shoots cleanly. There are some asymmetrical "pear-shaped" sling bullets which in fact are aerodynamically optimal, but they may be harder to shoot, and in any case need a bit of thought to load (which, in a combat situation may be less than ideal).
Why are modern bullets, for firearms, not shaped like a tear-drop ? I assume this is because they need a flat base for the propellant to actually act on the biggest surface possible.