I got it working... somehow.
While trying to narrow down the trouble I have, I updated with the latest testbuild found here: LibreELEC
It worked like a charm. The obvious difference I noticed: it's a tar file.
So I looked at the mirrors and found a 7.90.004 tar file. With this file the upgrade works without any problems.
Going back to an img or img.gz it fails with "SYSTEM or KERNEL" missing.
So there seems to be a problem with those files or with the update procedure.