Ginty reads The Greengage Summer when she's in the Upper Fifth and therefore presumably has access to the Limited section - maybe one of Rumer Godden's other adult novels? I can see the Kingscote staff not wanting the Thirds to innocently think 'Oh, that's by the same person who wrote Miss Happiness And Miss Flower' and pick up The Black Narcissus.

Alternatively, how about something by Joseph Conrad?