This is an interesting twist. When I came home tonight, I found the postman had delivered a thick envelope from our friends at Lantmäteriet.
Inside were all the papers I sent them as part of my application, each dutifully stamped and initialed in an official manner, plus a big detailed printout called a inskrivningsdagbok, which I translated as "enrollment diary".
It appears to me that everything has been officially approved and recorded, despite our rejection letter of earlier in the week.
I've sent scans of the inskrivningsdagbok to Tony and Rutger for their opinion. Stay tuned.
UPDATE: I talked to Rutger and my optimism was misplaced; our application is still "avslag", or rejected. We still need to submit a note from Ann-Catrin, which is on its way to me.