@zadocfish, you will commonly find that place is highly recommended to maximize the healing of your fairy. I recommend saving a video of one of your runs and monitor your fairies behavior when you view it. You will likely find moments where she's moving when she should be healing.

Now, that doesn't mean you must always place her, but the more you do it, the more relieving it will be knowing she's spamming embrace while you got free reign to do your thing.

It's like you said, being sch is almost like bringing two jobs into the instance. So keep that healer mentality intact, and try to place your fairy in the same position you would put yourself in if you were running as another healer.