Managed to find a workaround. If you restart ofono (sudo initctl restart ofono), the import suddenly starts working. The drawback is that your phone goes offline and you will have to restart to get it back online.
The pattern seems to be, that if your SIM is offline, import works. My 2nd SIM is blocked, therefore it stood offline and the import worked on the first try.
Unfortunately, switching to flight mode doesn't work, because it simulates a modem with no SIM card.