YAY, I've got it working - with new DMS and all!
I still think it's just applying your firmware - how long did you leave it?
Essentially, you are right. I tried to flash the box again and found out, that the reason for the trouble was the headunit. When I switched to the CD-Changer, the first patch was applied, the box rebooted but then the headunit hang, showing the "No CD-Changer"-message. In that state I could have waited forever.
I then had to switch to radio and back to CD to get the headunit to recognize the rebooted box, access it and apply the next patch. After a couple of switches the box played music, which I took as the successful application of the patch. And so it was.
Thanks for all the help, guys!