Hi, I did check small towns around Stockholm, it took me a day :) I checked suburbs and islands like tumba, tyreso, hasselby, danderyd, vaxholm etc.
I even checked some cities like Flen, Trosa and Nykoping which are 100 kilometers from Stockholm. But I can't see why someone would say they are from Stockholm when they come from Uppsala or something.
And Some of the church books are unreadable or nonexistent though, unfortunately.
He could also be an illegal immigrant, running away from doing the military service....
It seems strange that he never talked about his family or went back to visit them. But if he was an orphan he would still exist in the church books.