Just fyi, if someone has a similar issue than I had:
I identified the issue on my machine that seemed to cause the upgrade stop.
When I analyzed the software stack on my machine manually after not getting any meaningful info from MS, I noticed that the installed version of "8GadgetPack" was outdated (v29).
Since this tool was always inactivated during the last few win10 upgrades (I needed to update or at least reactivate the software afterwards manually), I thought that maybe the current version of the win upgrade tool might deal slightly different with this
software.
So I applied the latest version (v33) of 8GadgetPack and retried the "Windwows 10 Update-Assistent" afterwards.
This time the upgrade process worked.
I again had to reactivate 8GadgetPack afterwards - the upgrade inactivated the software same way it also happened during the last few successful win upgrades. But that was all.
I still don't know why I had to find this out by myself, without any info of the assistent, since such a software incompatibility should be easy to report by a tool. Anyhow...