Bad news: Turns out my Singer Featherweight has a broken part.
Good news: The zipper foot will work with the Brother I’ve been using up until now.
(Sadly, the narrow hemmer won’t, nor will the ruffler. Oh, I can’t wait to use all these fun attachments! But first: Must find a repair place. And in spite of its model name, the Singer is going to be a pain to haul around town.)