Morgo wanted to be a parental figure for Misfortune.
Unlike the rest of the kids he abducted, Morgo was genuinely fond of Misfortune. That would explain why he frequently chastised her on her language, did little favors like get a ticket for the carnival and asked that the player give her a good time. The problem is that he’s too controlling and possessive of Misfortune to know how to be a good parent for her.The "Eternal Happiness" reward being discussed was actually Misfortune spending eternity with Morgo.
Like the above entry, Morgo wanted to be a positive parental figure for Misfortune. He saw what a miserable life she was living and wanted to give her the life she deserved. He honestly thought she would be happy with him rather than her parents or Benjamin, which would explain his hostility.