Not exactly take advantage, I would say that she « hope » only good will come out of the situation, as the kid is in a bad situation (jour funeste)

Such expression is often seen in a bad situation, but that hope a good thing come out of there. In example;

« Elle a coulé son examen et elle risque de redoubler son année scolaire… J’espère qu’il n’en sortira que du bien… » Meaning that even if a bad thing happen, the person talking hope good thing will happen after such a fail, maybe the kid will now work harder and take more seriously his study, etc.

In the sentence "en sorte que" has nothing to do with the set expression "en sorte que". This combination is analysed differently in both cases. In the case of the locution there is no meaning to be given to "en" or "sorte"; the meaning is that of a set expression (tellement que, si bien que). On the contrary, in the sentence "sorte" is the verbe "sortir" conjugated in the subjunctive present and you give it the meaning it has usually; as well "en" is a pronoun and its antecedent is a situation, that of the young boy being suddenly turning to studying and books. However, it is difficult to extract this antecedent from the text; different people might tell you different things; this is an inherent problem with this type of "en" construction.

"Sortir de" means "to result from". So, what Mlle blumenthal is wishing for from this situation is that should result from it nothing else than good for the boy.

So, what Mlle Blumenthal is wishing for from this situation that is the antecedent of "en" should result nothing but good. Therefore, your understanding is correct.

Accurate translation:

• Qu’il n’en sorte que du bien, mon Dieu, qu’il n’en sorte que du bien.

• ne sortir que du bien de quelque chose =
• n’en sortir que du bien [The de quelque chose is replaced by en: of it or from it]

• May only something good come of it [or that], my God, may only something good come of it [or that].

Modernized: I hope only something good comes of it, etc.

Sortir is a verb here, and it’s in the subjunctive.

En is a pronoun that replaces "de quelque chose", which is probably given earlier in the text.

• Nothing good came of it. [some situation or other is assumed for all these example]

• Rien de bien n’en est sorti.

• Big problems came out of it.

• Des grands problèmes en sont sortis. [Big problems came out of it.]

So, [en] sortir always refers to something that comes out of something. The en is the pronoun that refers to whatever the antecedent is.

[en] sortir = to come out of something