It turned out that the flyballers were indeed the issue–thanks again @chazzycat–and a handful of competent groundballers was all the team needed to get their season turned around and back on track.
I made the changes mid-June, and as you can see the team have had their best 1.5 months of the season since, culminating in a 13-game win streak, the longest in the clubs history...
Due to their recent form, they've managed to claw their way off the bottom of their division, and the league overall, and turned an awful 19-35 into a much more respectable 51-53–especially considering their start!