IMO the problem with slingers in EB is not their stats, but the fact that their unit size is too big. Slinger units should be smaller than archer units. They were historically because the flatter trajectory of slingshots meant that slingers could not be packed as many ranks deep as archers, who could safely loose arrows in high arching trajectories over the heads of the forward ranks.
I changed the unit size of all slingers from 30 men to 20 men in the EDU. Bringing it down from 120 men to 80 men in Huge unit size. That reduced the unit's kill ratio to a more reasonable level for me. And I always deploy my slingers so that their formation is only 2 ranks deep.
I didn't change the unit costs because IMO slinging is harder and takes longer to learn than archery.