Booting the device yielded a storm of messages on the serial console, but then I was greeted with a password prompt. Luckily, the wiki page already had a description how to decrypt the config dump I obtained from the web interface earlier, and it contained the “support password” that was asked for as well.
I didn’t find anything that helped me, but at least I had fun tinkering with hardware and achieving something: The successful serial connection and even finding the right password. Of course I edited the OpenWRT wiki page to reflect my new findings and lately even received an email asking me for details (I couldn’t provide, but at least someone tried the serial approach).
Meanwhile I bought an AVM FRITZ!Box 7390, the latest and greatest model of the best German vendor for home DSL routers in my opinion, because the IAD had problems with some UDP streams (especially OpenVPN) and didn’t allow third-party VoIP accounts. I’m happy with the quite costly change, the FRITZ!Box was worth its money I guess.