Is [骨を折ってみる約束] working as an adverbial construction for 「六蔵の教育をして」, or is it somehow closer to [六蔵の教育を骨を折ってみる約束として]? the meaning I extract out of the bolded part is ,( limited to what I know) : [... "laborious" attempt of undergoing the rokuzou tranining/education ...]
Is it (adapted translation) "at that time, I promised the pitiful woman to work hard on rokuzou's education, after dispatching her, the same night I stayed awake untill late, "trying" to figure out how(a plan to do so)" ?
I knew I'd have at least ONE error in my transcription....
"Having promised the pitiable woman to spare no efforts in attempting to educate her son, I sent Rokuzou's mother away and stayed awake late that night, turning over in my head various ideas."
Or some variation thereof.
Some of you might like to try reading this story. It is neither long nor difficult and the good folks at Aozora Bunko have modernized the kanji and kana usage. Available on Amazon for the Kindle (free!) or from Aozora Bunko.