One thing that might help your pitching is if you carried 7 or even 8 relievers instead of six. Chazzycat mentioned earlier in this thread that you can keep just a backup IF, OF, C, and an extra PH/DH if you like. I probably wouldn't go with just three backups unless I had a player like Javy Baez on my bench, but even if you were to simply remove your 5th OF in favor of a 7th reliever you would spread the relief workload out and give some of the other guys extra rest if they need it.
My bullpen usually consists of a long reliever, three middle relievers, a 7th inning guy, an 8th inning guy, and my closer. Depending on the situation (park factors, league opponents), I might prioritize a lefty specialist over a second setup man. Also consider adjusting when your manager hooks your pitchers, if you haven't already.
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