Today I received an MicroSD card from a different brand, unpacked it, copied the latest firmware and it worked.
All my other cards are SanDisk, mostly 32GB Ultra A1 but also one 256GB Extreme A2. They all start just fine into the menu and work with games.
That new card is just an PNY 16GB Elite class 10 UHS-I. Is there a chance that the modern SanDisk cards are in some way to fast?
Thanks again for all your input and the great GameDrive! If you want to investigate further and have me test something, just let me know.