like today there would probably have been no fixed style.
The roman legionnaires would have been drilled in a given style, no doubt. But the average slinger wasn't a full time soldier so would most likely use whatever style they were most comfortable with.
And for battle formation, overhead is just not practical.
It takes up a lot of space, it's slow between shots, and it raises the chance of a missile going sideways, or behind.
A fig 8 type style or balearic sidearm is far more practical, useful and less potentially lethal to your colleagues.
You can pack slingers doing fig 8 3-4 feet apart quite safely (all these things I've tested in the field - well up a hillfort anyway
, length of sling is largely irrelevant.
So short sling with heavy rocks for close up or longer slings with lead bullets don't require more space per slinger.
10-12 shots a minute is easily achieved without rushing and can be kept up all day with out strain (tested that one in the rain, 20mph winds and sleet).
It's also far more easy to be accurate and powerful at the same time.
I can't think of any positives for helicopter style in combat.
Helicopter is just not practical under battle conditions, unless there are very few of you spaced a long way apart.
But even then just about every other style is better for combat.
Our ancestors weren't primitives or idiots, and they were far more practical and skilled than any of us will ever be. The sling was an every day tool and you can bet every last silver owl in greece that their slinging style was efficient, effective and practical.