I can stop worrying about not getting the visa in time. The good people at the American embassy must have outperformed themselves. Instead of “about a week” it took two days before I had my passport back with the visa in it!
I even got the photo back attached to the passport with a paper clip. Instead they used the picture that I uploaded together with the form I filled in online. They preferred a picture I had taken of myself at home over a picture taken by a professional photographer that costed me 200 SEK. Well well… Maybe I can use the picture for the California drivers license later instead.