SCH DPS optimization

[Typhoria]

Are you using consumables? Food buff + Mind Potions?

[Hysterior]

Well I dont have the best equipment yet either but for now I want to focus on my rotation as it will take some time to change muscle memory

[Typhoria]

Your play might not even be the issue really.
First thing is you need a group that allows you to maximize doing DPS GCDs, as in they don't get hit by avoidable mechanics much. Second the other healer covers the bulk of healing where you might clip a GCD. Organized groups are preferred for top parses since you never know the quality of pugs.

In terms of "rotation", keep Biolysis up on as many targets as possible assuming they will live the full duration of the DoT. During that GCD you can weave oGCDs in for healing. Broil spam on single targets only if you don't have to move, Art of War is better when you can hit 2 or more assuming there is no MP issue. If you absolutely have to move use Ruin II if Biolysis isn't needed to be recast, this will also give you a oGCD window to weave. Don't forget about weaving in Chain Stratagem during the group DPS window.

Check the top Scholar on Innocence, he did low healing while the other carried the weight on that. Additionally, he was dance partnered and had a second scholar for another Chain Stratagem.