You would have got the letter long before you finished a house if you were entitled to one. Good for you, obviously killing little old ladies is not your style, or you missed that quest. So the question is, what are you willing to do to adopt from the orphanage? There are plenty of other orphans in Skyrim, if you really want one without murdering someone.
And if someone has found some other way to adopt from the orphanage I would love to hear it.