I'm going to repeat stuff I've mentioned before - because this, completely over the top, buff to slingers will once more imbalance the game.....
Very experienced, highly trained and definitely individual, slingers can achieve rather exceptional long ranges. Ranges that can indeed be longer than the relatively poor bows commonly found due to the inherent mechanical limitations they have.
The ranges we should consider are those that are considered effective - especially when used in formed bodies of men. Slingers (and indeed bowmen), with very few exceptions, are in the extreme minority numbers in almost any ancient battle. We should, indeed, only have a very restricted mercenary supply from places like the Balaerics and Rhodes (famed for their slingers); ditto Crete for their archers.
No Roman army (sic) of our entire period (and others are similar) should have more than a single unit of slingers - and they should be hard to come by.
If slingers are as effective as dear old Wiki would imply (and people then erroneously support); then Napoleonic armies would have used slingers - for they would have been more effective. Hell, we should have maintained the old laws in England and Wales and Wellington would have used longbows!
Why didn't they - because men of that experience and skill level are available in very small numbers.........
TL
R - this change should be entirely undone and will imbalance the game - making it that much poorer.