I would disagree about the slinger/shield situation.
We know javelin skirmishers carried a shield. Archers cant use a shield but slingers certainly can. And slingers need shields because...?
My hypothesis is that the opening ranged volleys from skirmishers were not initially directed against the enemy heavy infantry but against their skirmish line. These are, after all, the first enemy units to come into range as the armies close on each other.
The slingers and archers are then embroiled in a ferocious firefight against each other for posession of the shrinking centre ground. The javelin throwers are not in range yet and stay well back, probably just in front of the main infantry.
If your sides slingers and archers prevail then you have a big advantage during the next stage, which is the javelin rush. When the enemy infantry is close enough, the javelin throwers charge across the centre ground and start hurling their weapons. This is the first time the main infantry has been targeted, because the javelin is the first weapon that can inflict real damage on heavily armoured and shielded formations.
The focus of the skirmishing battle is to win dominance of the centre ground for your javelin rush. If you lose that dominance, then your javelin men will have to charge into the teeth of enemy slingers and archers, who are able to shoot diagonally thanks to their much greater ranges and thus create a hellish crossfire that a single shield cannot protect against.
After several volleys of javelins with the armies getting perilously close together, its time to get the heck out of the way. The skirmishers near the flanks can run around the ends of their lines but the ones in the middle have to move back through their own infantry. Thats easy enough, if you put up a good show and kept the enemy javelins away from your infantry, they will gladly move aside and let you through. If you sucked, and the enemies javelins have inflicted serious casualties... forget it. You're toast.