That seems to have worked - thank you!
KB3020369 showed some quirks while installing, the Standalone Installer would, in some situations, again never finish checking "updates on this computer".
Finally starting the installation after a clean restart did the magic.
KB3161647 the installed with no problem, after which I could find and install updates.
At some point a update recheck reported error #80244019, that one disappeared after a restart and I could install the last update batch.
Thank you again, I hope this topic can be finished now! :)